Airfoil shape for a compressor

ABSTRACT

An article of manufacture having a nominal airfoil profile substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in a scalable table, the scalable table selected from the group of tables consisting of TABLES 1-2, wherein the Cartesian coordinate values of X, Y and Z are non-dimensional values convertible to dimensional distances by multiplying the Cartesian coordinate values of X, Y and Z by a number, and wherein X and Y are coordinates which, when connected by continuing arcs, define airfoil profile sections at each Z height, the airfoil profile sections at each Z height being joined with one another to form a complete airfoil shape.

RELATED APPLICATIONS

The present application is related to Ser. Nos. 13/526,832, 13/526,863, 13/526,920 and 13/526,941 filed concurrently herewith, which are each fully incorporated by reference herein and made a part hereof.

BACKGROUND OF THE INVENTION

The present invention relates generally to an airfoil for use in turbomachinery, and more particularly relates to an airfoil profile or airfoil shape for use in a compressor.

In turbomachines, many system requirements should be met at each stage of the turbomachine's flow path to meet design goals. These design goals include, but are not limited to, overall improved efficiency, reduction of vibratory response and improved airfoil loading capability. For example, a compressor airfoil profile should achieve thermal and mechanical operating requirements for a particular stage in the compressor. Moreover, component lifetime, reliability and cost targets also should be met.

BRIEF DESCRIPTION OF THE INVENTION

According to one aspect of the present invention an article of manufacture is provided having a nominal airfoil profile substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in a scalable table, the scalable table selected from the group of tables consisting of TABLES 1-2, wherein the Cartesian coordinate values of X, Y and Z are non-dimensional values convertible to dimensional distances by multiplying the Cartesian coordinate values of X, Y and Z by a number, and wherein X and Y are coordinates which, when connected by continuing arcs, define airfoil profile sections at each Z height, the airfoil profile sections at each Z height being joined smoothly with one another to form a complete airfoil shape.

According to another aspect of the present invention an article of manufacture is provided having a suction-side nominal airfoil profile substantially in accordance with suction-side Cartesian coordinate values of X, Y and Z set forth in a scalable table, the scalable table selected from the group of tables consisting of TABLES 1-2, wherein the Cartesian coordinate values of X, Y and Z are non-dimensional values convertible to dimensional distances by multiplying the Cartesian coordinate values of X, Y and Z by a number, and wherein X and Y are coordinates which, when connected by continuing arcs, define airfoil profile sections at each Z height, the airfoil profile sections at each Z height being joined smoothly with one another to form a complete suction-side airfoil shape, the X, Y and Z coordinate values being scalable as a function of the number to provide at least one of a non-scaled, scaled-up and scaled-down airfoil profile.

According to yet another aspect of the present invention a compressor is provided comprising a plurality of variable stator vanes, each of the variable stator vanes including an airfoil having a suction-side airfoil shape, the airfoil having a nominal profile substantially in accordance with suction-side Cartesian coordinate values of X, Y and Z set forth in a scalable table, the scalable table selected from the group of tables consisting of TABLES 1-2, wherein the Cartesian coordinate values of X, Y and Z are non-dimensional values convertible to dimensional distances by multiplying the Cartesian coordinate values of X, Y and Z by a number, and wherein X and Y are coordinates which, when connected by continuing arcs, define airfoil profile sections at each Z height, the airfoil profile sections at each Z height being joined smoothly with one another to form a complete suction-side airfoil shape.

These and other features and improvements of the present invention should become apparent to one of ordinary skill in the art upon review of the following detailed description when taken in conjunction with the several drawings and the appended claims.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic representation of a compressor flow path through multiple stages and illustrates exemplary compressor stages according to an aspect of the invention;

FIG. 2 is a perspective view of an variable stator vane, according to an aspect of the invention; and

FIG. 3 is a cross-sectional view of the variable stator vane airfoil taken generally about on line 3-3 in FIG. 2, according to an aspect of the present invention.

DETAILED DESCRIPTION OF THE INVENTION

One or more specific aspects/embodiments of the present invention will be described below. In an effort to provide a concise description of these aspects/embodiments, all features of an actual implementation may not be described in the specification. It should be appreciated that in the development of any such actual implementation, as in any engineering or design project, numerous implementation-specific decisions must be made to achieve the developers' specific goals, such as compliance with machine-related, system-related and business-related constraints, which may vary from one implementation to another. Moreover, it should be appreciated that such a development effort might be complex and time consuming, but would nevertheless be a routine undertaking of design, fabrication, and manufacture for those of ordinary skill having the benefit of this disclosure.

When introducing elements of various embodiments of the present invention, the articles “a,” “an,” “the,” and “said” are intended to mean that there are one or more of the elements. The terms “comprising,” “including,” and “having” are intended to be inclusive and mean that there may be additional elements other than the listed elements. Any examples of operating parameters and/or environmental conditions are not exclusive of other parameters/conditions of the disclosed embodiments. Additionally, it should be understood that references to “one embodiment”, “one aspect” or “an embodiment” or “an aspect” of the present invention are not intended to be interpreted as excluding the existence of additional embodiments or aspects that also incorporate the recited features. Turbomachinery is defined as one or more machines that transfer energy between a rotor and a fluid or vice-versa, including but not limited to gas turbines, steam turbines and compressors.

Referring now to the drawings, FIG. 1 illustrates an axial compressor flow path 1 of a compressor 2 that includes a plurality of compressor stages. The compressor 2 may be used in conjunction with, or as part of a gas turbine. As one non-limiting example only, the compressor flow path 1 may comprise about eighteen rotor/stator stages. However, the exact number of rotor and stator stages is a choice of engineering design, and may be more or less than the illustrated eighteen stages. It is to be understood that any number of rotor and stator stages can be provided in the compressor, as embodied by the invention. The eighteen stages are merely exemplary of one turbine/compressor design, and are not intended to limit the invention in any manner.

The compressor rotor blades 22 impart kinetic energy to the airflow and therefore bring about a desired pressure rise. Directly following the rotor blades 22 is a stage of stator compressor vanes 23. However, in some designs the stator vanes may precede the rotor blades. Both the rotor blades and stator vanes turn the airflow, slow the airflow velocity (in the respective airfoil frame of reference), and yield a rise in the static pressure of the airflow. Typically, multiple rows of rotor/stator stages are arranged in axial flow compressors to achieve a desired discharge to inlet pressure ratio. Each rotor blade and stator vane includes an airfoil, and these airfoils can be secured to rotor wheels or a stator case by an appropriate attachment configuration, often known as a “root,” “base” or “dovetail” (not shown). In addition, compressors may also include inlet guide vanes (IGVs) 21, variable stator vanes (VSVs) 25 and exit or exhaust guide vanes (EGVs) 27. All of these blades and vanes have airfoils that act on the medium (e.g., air) passing through the compressor flow path 1.

Exemplary stages of the compressor 2 are illustrated in FIG. 1. One stage of the compressor 2 comprises a plurality of circumferentially spaced rotor blades 22 mounted on a rotor wheel 51 and a plurality of circumferentially spaced stator vanes 23 attached to a static compressor case 59. Each of the rotor wheels 51 may be attached to an aft drive shaft 58, which may be connected to the turbine section of the engine. The rotor blades 22 and stator vanes 23 lie in the flow path 1 of the compressor 2. The direction of airflow through the compressor flow path 1, as embodied by the invention, is indicated by the arrow 60 (FIG. 1), and flows generally front left to right in the illustration. The rotor blades and stator vanes herein of the compressor 2 are merely exemplary of the stages of the compressor 2 within the scope of the invention. In addition, each inlet guide vane 21, rotor blade 22, stator vane 23, variable stator vane 25 and exit guide vane 27 may be considered an article of manufacture. Further, the article of manufacture may comprise a variable stator vane configured for use with a compressor.

A variable stator vane 25, illustrated in FIG. 2, is provided with an airfoil 200. Each of the variable stator vanes 25 has an airfoil profile at any cross-section from the airfoil root 220 to the airfoil tip 210. Referring to FIG. 3, it will be appreciated that each variable stator vane 25 has an airfoil 200 as illustrated. The airfoil 200 has a suction side 310 and a pressure side 320. The suction side 310 is located on the opposing side of the airfoil from the pressure side 320. Thus, each of the variable stator vanes 25 has an airfoil profile at any cross-section in the shape of the airfoil 200. The airfoil 200 also includes a leading edge 330 and a trailing edge 340, and a chord length 350 extends therebetween. The root of the airfoil corresponds to the lowest non-dimensional Z value of scalable Table 1. The tip of the airfoil corresponds to the highest non-dimensional Z value of scalable Table 1. An airfoil may extend beyond the compressor flowpath and may be tipped to achieve the desired endwall clearances. As non-limiting examples only, the height of the airfoil 200 may be from about 1 inch to about 30 inches or more, about 5 inches to about 20 inches, about 5 inches to about 15 inches, or about 10 inches to about 15 inches. However, any specific airfoil height may be used as desired in the specific application.

The compressor flow path 1 requires airfoils that meet system requirements of aerodynamic and mechanical blade/vane loading and efficiency. For example, it is desirable that the airfoils are designed to reduce the vibratory response or vibratory stress response of the respective blades and/or vanes. Materials such as high strength alloys, non-corrosive alloys and/or stainless steels may be used in the blades and/or vanes. To define the airfoil shape of each blade airfoil and/or vane airfoil, there is a unique set or loci of points in space that meet the stage requirements and can be manufactured. These unique loci of points meet the requirements for stage efficiency and are arrived at by iteration between aerodynamic and mechanical loadings enabling the turbine and compressor to run in an efficient, safe, reliable and smooth manner. These points are unique and specific to the system. The locus that defines the airfoil profile includes a set of points with X, Y and Z coordinates relative to a reference origin coordinate system. The three-dimensional Cartesian coordinate system of X, Y and Z values given in scalable Tables 1-2 below defines the profile of the variable stator vane airfoil at various locations along its length. Scalable Tables 1-2 list data for a non-coated airfoil. The envelope/tolerance for the coordinates is about +/−5% of the chord length 350 in a direction normal to any airfoil surface location, or about +/−0.25 inches in a direction normal to any airfoil surface location. However, tolerances of about +/−0.15 inches to about +/−0.25 inches, or about +/−3% to about +/−5% in a direction normal to an airfoil surface location may also be used, as desired in the specific application.

The point data origin 230 may be the mid-point of the suction or pressure side of the base of the airfoil, the leading edge or trailing edge of the base of the airfoil, or any other suitable location as desired. The coordinate values for the X, Y and Z coordinates are set forth in non-dimensionalized units in scalable Tables 1-2, although other units of dimensions may be used when the values are appropriately converted. As one example only, the Cartesian coordinate values of X, Y and Z may be convertible to dimensional distances by multiplying the X, Y and Z values by a multiplying by a constant number (e.g., 100). The number, used to convert the non-dimensional values to dimensional distances, may be a fraction (e.g., ½, ¼, etc.), decimal fraction (e.g., 0.5, 10.25, etc.), integer (e.g., 1, 2, 10, 100, etc.) or a mixed number (e.g., 1½, 10¼, etc.). The dimensional distances may be any suitable format (e.g., inches, feet, millimeters, centimeters, meters, etc.). As one non-limiting example only, the Cartesian coordinate system has orthogonally-related X, Y and Z axes and the X axis may lie generally parallel to the compressor rotor centerline, i.e., the rotary axis and a positive X coordinate value is axial toward the aft, i.e., exhaust end of the turbine. The positive Y coordinate value extends tangentially in the direction of rotation of the rotor and the positive Z coordinate value is radially outwardly toward the rotor blade tip, variable stator vane or stator vane base. All the values in scalable Tables 1 and 2 are given at room temperature and are unfilleted.

By defining X and Y coordinate values at selected locations in a Z direction (or height) normal to the X, Y plane, the profile section or airfoil shape of the airfoil, at each Z height along the length of the airfoil can be ascertained. By connecting the X and Y values with smooth continuing arcs, each profile section at each Z height is fixed. The airfoil profiles of the various surface locations between each Z height are determined by smoothly connecting the adjacent profile sections to one another to form the airfoil profile.

The Table 1 and Table 2 values are generated and shown from zero to four or more decimal places for determining the profile of the airfoil. As the airfoil heats up the associated stress and temperature will cause a change in the X, Y and Z values. Accordingly, the values for the profile given in Table 1 and Table 2 represent ambient, non-operating or non-hot conditions e.g., room temperature) and are for an uncoated airfoil.

There are typical manufacturing tolerances as well as optional coatings which must be accounted for in the actual profile of the airfoil. Each section is joined smoothly with the other sections to form the complete airfoil shape. It will therefore be appreciated that +/− typical manufacturing tolerances, +/− values, including any coating thicknesses, are additive to the X and Y values given in Tables 1-2 below. Accordingly, a distance of about +/−5% of chord length and/or +/−0.25 inches in a direction normal to a surface location along the airfoil profile defines an airfoil profile envelope for this particular airfoil design and compressor, i.e., a range of variation between measured points on the actual airfoil surface at nominal cold or room temperature and the ideal position of those points as given in the Tables below at the same temperature. Additionally, a distance of about +/−5% of a chord length in a direction normal to an airfoil surface location along the airfoil profile also may define on airfoil profile envelope for this particular airfoil design. The data is scalable and the geometry pertains to all aerodynamic scales, at, above and/or below about 3,600 RPM. The variable stator vane airfoil design is robust to this range of variation without impairment of mechanical and aerodynamic functions.

The coordinate values given in scalable TABLE 1 below provide the nominal profile for an exemplary stage compressor variable stator vane,

TABLE 1 SUCTION SIDE PRESSURE SIDE X Y Z X Y Z −1.44026 1.868152 −0.59855 2.3552 −1.59997 −0.59855 −1.4478 1.864012 −0.59855 2.355568 −1.59905 −0.59855 −1.45618 1.8561 −0.59855 2.356304 −1.59712 −0.59855 −1.464 1.843956 −0.59855 2.3575 −1.59316 −0.59855 −1.47053 1.82804 −0.59855 2.35888 −1.58507 −0.59855 −1.47605 1.805684 −0.59855 2.358696 −1.57228 −0.59855 −1.48 1.776336 −0.59855 2.350968 −1.55066 −0.59855 −1.48175 1.739352 −0.59855 2.32852 −1.52968 −0.59855 −1.48092 1.694364 −0.59855 2.294664 −1.50576 −0.59855 −1.47697 1.640912 −0.59855 2.252436 −1.47568 −0.59855 −1.46961 1.579088 −0.59855 2.197604 −1.43658 −0.59855 −1.4571 1.506684 −0.59855 2.1344 −1.39122 −0.59855 −1.43897 1.423976 −0.59855 2.067056 −1.34274 −0.59855 −1.41468 1.331056 −0.59855 1.991432 −1.288 −0.59855 −1.38423 1.227924 −0.59855 1.90762 −1.227 −0.59855 −1.34624 1.115316 −0.59855 1.815712 −1.15948 −0.59855 −1.29886 0.994888 −0.59855 1.720124 −1.08836 −0.59855 −1.2455 0.871148 −0.59855 1.620856 −1.01329 −0.59855 −1.18533 0.744556 −0.59855 1.518184 −0.93435 −0.59855 −1.11697 0.615756 −0.59855 1.4122 −0.85109 −0.59855 −1.04052 0.484748 −0.59855 1.303088 −0.76351 −0.59855 −0.95542 0.351716 −0.59855 1.190848 −0.67142 −0.59855 −0.86158 0.21758 −0.59855 1.07548 −0.57491 −0.59855 −0.75955 0.08372 −0.59855 0.957168 −0.47389 −0.59855 −0.65274 −0.04554 −0.59855 0.839684 −0.37196 −0.59855 −0.54133 −0.17038 −0.59855 0.72266 −0.26938 −0.59855 −0.42513 −0.29063 −0.59855 0.605912 −0.16661 −0.59855 −0.30461 −0.40664 −0.59855 0.48898 −0.06394 −0.59855 −0.17986 −0.5186 −0.59855 0.371496 0.037996 −0.59855 −0.04913 −0.62486 −0.59855 0.25346 0.13938 −0.59855 0.08786 −0.72487 −0.59855 0.136528 0.24196 −0.59855 0.229264 −0.81797 −0.59855 0.021528 0.346656 −0.59855 0.373796 −0.90427 −0.59855 −0.09218 0.452732 −0.59855 0.521088 −0.98449 −0.59855 −0.20433 0.560464 −0.59855 0.670956 −1.05938 −0.59855 −0.31492 0.669852 −0.59855 0.817972 −1.127 −0.59855 −0.42026 0.777124 −0.59855 0.961676 −1.18855 −0.59855 −0.52044 0.882188 −0.59855 1.101792 −1.24458 −0.59855 −0.61557 0.984952 −0.59855 1.237952 −1.29582 −0.59855 −0.70573 1.085048 −0.59855 1.369972 −1.34283 −0.59855 −0.79111 1.182476 −0.59855 1.497576 −1.38607 −0.59855 −0.87198 1.277052 −0.59855 1.620488 −1.426 −0.59855 −0.94815 1.368868 −0.59855 1.738616 −1.46298 −0.59855 −1.01724 1.452956 −0.59855 1.846164 −1.49574 −0.59855 −1.07962 1.529224 −0.59855 1.943132 −1.52481 −0.59855 −1.1351 1.597672 −0.59855 2.029428 −1.55038 −0.59855 −1.18441 1.65784 −0.59855 2.110388 −1.57403 −0.59855 −1.2282 1.709084 −0.59855 2.180584 −1.59445 −0.59855 −1.26638 1.751404 −0.59855 2.234588 −1.61009 −0.59855 −1.30014 1.786548 −0.59855 2.277828 −1.6227 −0.59855 −1.32977 1.814976 −0.59855 2.31058 −1.63033 −0.59855 −1.35534 1.836872 −0.59855 2.335052 −1.62362 −0.59855 −1.37715 1.852696 −0.59855 2.346092 −1.61451 −0.59855 −1.39509 1.862908 −0.59855 2.35152 −1.60715 −0.59855 −1.40962 1.86852 −0.59855 2.353728 −1.60319 −0.59855 −1.42241 1.870912 −0.59855 2.35474 −1.60108 −0.59855 −1.43281 1.87036 −0.59855 −1.48792 1.915624 0 2.460908 −1.411 0 −1.49509 1.910932 0 2.461276 −1.40999 0 −1.50273 1.902376 0 2.462012 −1.40806 0 −1.50935 1.88968 0 2.463208 −1.4041 0 −1.51423 1.873304 0 2.464588 −1.39601 0 −1.51763 1.850764 0 2.464036 −1.38313 0 −1.51874 1.821324 0 2.455296 −1.36178 0 −1.5169 1.784616 0 2.43156 −1.342 0 −1.51174 1.74018 0 2.396784 −1.31919 0 −1.50282 1.687832 0 2.35336 −1.29048 0 −1.48985 1.627388 0 2.296964 −1.25313 0 −1.47108 1.556824 0 2.23192 −1.20989 0 −1.44606 1.476508 0 2.162736 −1.16362 0 −1.41432 1.386348 0 2.085088 −1.11118 0 −1.37586 1.286436 0 1.999068 −1.05257 0 −1.32986 1.177968 0 1.90486 −0.98762 0 −1.27438 1.062232 0 1.806788 −0.91908 0 −1.21284 0.943736 0 1.704944 −0.84686 0 −1.14448 0.822848 0 1.599512 −0.77059 0 −1.0684 0.70012 0 1.490676 −0.69046 0 −0.98458 0.575552 0 1.378344 −0.606 0 −0.89277 0.44942 0 1.2627 −0.51741 0 −0.79221 0.322 0 1.143744 −0.4244 0 −0.68301 0.193936 0 1.021568 −0.32715 0 −0.56957 0.070472 0 0.90022 −0.22899 0 −0.452 −0.04839 0 0.779332 −0.13018 0 −0.33037 −0.16284 0 0.65872 −0.0311 0 −0.20498 −0.27306 0 0.538016 0.067988 0 −0.07544 −0.37876 0 0.416944 0.16652 0 0.059156 −0.47886 0 0.295504 0.264592 0 0.198904 −0.57298 0 0.174708 0.363584 0 0.342148 −0.66074 0 0.055292 0.46414 0 0.48806 −0.74235 0 −0.06284 0.566168 0 0.636272 −0.81862 0 −0.17977 0.669576 0 0.786508 −0.88992 0 −0.2955 0.774364 0 0.933616 −0.95478 0 −0.40609 0.877036 0 1.077044 −1.01384 0 −0.51161 0.9775 0 1.2167 −1.06784 0 −0.61217 1.075572 0 1.352216 −1.11752 0 −0.70785 1.171252 0 1.483316 −1.16316 0 −0.79884 1.264264 0 1.61 −1.20529 0 −0.88522 1.354424 0 1.731992 −1.2443 0 −0.9672 1.441548 0 1.849108 −1.28046 0 −1.04162 1.521496 0 1.95592 −1.31247 0 −1.10878 1.594176 0 2.052336 −1.34072 0 −1.1684 1.659404 0 2.13808 −1.36528 0 −1.2213 1.716904 0 2.218672 −1.3881 0 −1.26794 1.765848 0 2.2885 −1.40751 0 −1.30842 1.806328 0 2.34232 −1.42232 0 −1.34384 1.840092 0 2.385376 −1.4341 0 −1.37476 1.86714 0 2.417944 −1.4409 0 −1.40134 1.888024 0 2.441588 −1.43382 0 −1.42398 1.902928 0 2.452168 −1.4249 0 −1.44238 1.912312 0 2.457412 −1.4179 0 −1.45719 1.917372 0 2.459528 −1.41404 0 −1.47007 1.919212 0 2.460448 −1.41202 0 −1.48046 1.9182 0 −1.54376 1.983336 0.72818 2.583728 −1.17015 0.72818 −1.55038 1.978092 0.72818 2.584096 −1.16914 0.72818 −1.55701 1.968984 0.72818 2.584832 −1.1672 0.72818 −1.56216 1.955828 0.72818 2.585936 −1.16325 0.72818 −1.5652 1.939176 0.72818 2.587224 −1.15506 0.72818 −1.56593 1.916728 0.72818 2.586396 −1.14209 0.72818 −1.56354 1.88784 0.72818 2.576368 −1.1212 0.72818 −1.55728 1.852052 0.72818 2.551252 −1.1029 0.72818 −1.5468 1.80918 0.72818 2.515372 −1.08128 0.72818 −1.53189 1.75904 0.72818 2.470568 −1.05423 0.72818 −1.51239 1.701172 0.72818 2.412332 −1.01908 0.72818 −1.48654 1.633828 0.72818 2.345172 −0.97833 0.72818 −1.45388 1.5571 0.72818 2.27378 −0.93463 0.72818 −1.41395 1.471356 0.72818 2.19374 −0.88495 0.72818 −1.36694 1.37678 0.72818 2.105144 −0.82929 0.72818 −1.31247 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0.913192 0.72818 1.052112 −0.72551 0.72818 −0.39128 1.010344 0.72818 1.19692 −0.78274 0.72818 −0.50287 1.105196 0.72818 1.337496 −0.83518 0.72818 −0.60959 1.197748 0.72818 1.473656 −0.88357 0.72818 −0.71162 1.287816 0.72818 1.605216 −0.92828 0.72818 −0.80877 1.375308 0.72818 1.732084 −0.96968 0.72818 −0.90151 1.459948 0.72818 1.854076 −1.00814 0.72818 −0.99029 1.541184 0.72818 1.9711 −1.04383 0.72818 −1.07079 1.61598 0.72818 2.077728 −1.0753 0.72818 −1.14328 1.68406 0.72818 2.17396 −1.1028 0.72818 −1.20778 1.745332 0.72818 2.259612 −1.12672 0.72818 −1.26482 1.799152 0.72818 2.34002 −1.1488 0.72818 −1.31477 1.845336 0.72818 2.409848 −1.16757 0.72818 −1.35783 1.883608 0.72818 2.463576 −1.18174 0.72818 −1.39518 1.915532 0.72818 2.506724 −1.19287 0.72818 −1.42766 1.941108 0.72818 2.5392 −1.19986 0.72818 −1.45544 1.960612 0.72818 2.56358 −1.19333 0.72818 −1.47899 1.97432 0.72818 2.57462 −1.1845 0.72818 −1.49804 1.982784 0.72818 2.580048 −1.17723 0.72818 −1.51312 1.987016 0.72818 2.582256 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2.908948 −0.54804 1.702184 2.908948 1.457648 0.031372 2.908948 −0.66056 1.784064 2.908948 1.589944 −0.01306 2.908948 −0.76829 1.863644 2.908948 1.71764 −0.05428 2.908948 −0.87124 1.9412 2.908948 1.840644 −0.09264 2.908948 −0.96977 2.016088 2.908948 1.958864 −0.12852 2.908948 −1.06462 2.087112 2.908948 2.072116 −0.1621 2.908948 −1.15101 2.15234 2.908948 2.175248 −0.19191 2.908948 −1.22838 2.212508 2.908948 2.26826 −0.21822 2.908948 −1.29711 2.266788 2.908948 2.350968 −0.24122 2.908948 −1.35774 2.314812 2.908948 2.428708 −0.26248 2.908948 −1.41045 2.356212 2.908948 2.496052 −0.28069 2.908948 −1.45526 2.390988 2.908948 2.54794 −0.29449 2.908948 −1.4938 2.420336 2.908948 2.589432 −0.30553 2.908948 −1.52683 2.444164 2.908948 2.62062 −0.31354 2.908948 −1.55489 2.46238 2.908948 2.643988 −0.31041 2.908948 −1.57835 2.475444 2.908948 2.654752 −0.30259 2.908948 −1.59712 2.483816 2.908948 2.659996 −0.29596 2.908948 −1.61193 2.488324 2.908948 2.662112 −0.29219 2.908948 −1.62472 2.48998 2.908948 2.66294 −0.29026 2.908948 −1.63484 2.488508 2.908948 −1.65094 2.620252 3.63584 2.630464 −0.07728 3.63584 −1.65591 2.613904 3.63584 2.63074 −0.07636 3.63584 −1.65867 2.603508 3.63584 2.631384 −0.07434 3.63584 −1.65858 2.590076 3.63584 2.632212 −0.07047 3.63584 −1.65572 2.574344 3.63584 2.632672 −0.06228 3.63584 −1.64956 2.554012 3.63584 2.629728 −0.05005 3.63584 −1.63916 2.528344 3.63584 2.61464 −0.0334 3.63584 −1.62408 2.49734 3.63584 2.587224 −0.01996 3.63584 −1.60393 2.460724 3.63584 2.550608 −0.00212 3.63584 −1.57835 2.418036 3.63584 2.504884 0.02024 3.63584 −1.54744 2.368724 3.63584 2.445452 0.049404 3.63584 −1.50963 2.311132 3.63584 2.377004 0.083352 3.63584 −1.46455 2.245904 3.63584 2.30414 0.119784 3.63584 −1.41192 2.173132 3.63584 2.222168 0.160816 3.63584 −1.35194 2.092908 3.63584 2.131088 0.20654 3.63584 −1.28432 2.00514 3.63584 2.03136 0.2576 3.63584 −1.20732 1.911576 3.63584 1.927584 0.31188 3.63584 −1.12323 1.816816 3.63584 1.819852 0.369564 3.63584 −1.03307 1.7204 3.63584 1.70798 0.430468 3.63584 −0.93656 1.622328 3.63584 1.592152 0.494592 3.63584 −0.8337 1.523704 3.63584 1.472552 0.562212 3.63584 −0.72441 1.42508 3.63584 1.348996 0.63342 3.63584 −0.60876 1.326548 3.63584 1.22176 0.708216 3.63584 −0.48659 1.228108 3.63584 1.090844 0.786692 3.63584 −0.36184 1.133164 3.63584 0.96048 0.86618 3.63584 −0.2346 1.041992 3.63584 0.83076 0.94668 3.63584 −0.10488 0.954132 3.63584 0.701408 1.028008 3.63584 0.0276 0.870136 3.63584 0.572516 1.109888 3.63584 0.162932 0.79028 3.63584 0.4439 1.192228 3.63584 0.301208 0.714472 3.63584 0.315376 1.274752 3.63584 0.44206 0.642344 3.63584 0.186852 1.357276 3.63584 0.58512 0.573712 3.63584 0.058604 1.440168 3.63584 0.729744 0.508668 3.63584 −0.06909 1.524072 3.63584 0.875748 0.446844 3.63584 −0.19605 1.608896 3.63584 1.02304 0.387964 3.63584 −0.32246 1.694732 3.63584 1.166468 0.3335 3.63584 −0.4439 1.778636 3.63584 1.305756 0.283268 3.63584 −0.56056 1.860516 3.63584 1.44072 0.236624 3.63584 −0.6727 1.939912 3.63584 1.571268 0.193292 3.63584 −0.78034 2.0171 3.63584 1.697216 0.153088 3.63584 −0.88302 2.092264 3.63584 1.818564 0.115644 3.63584 −0.98118 2.165036 3.63584 1.935036 0.080592 3.63584 −1.07585 2.233944 3.63584 2.046632 0.047656 3.63584 −1.16214 2.297056 3.63584 2.148292 0.018124 3.63584 −1.23942 2.3552 3.63584 2.239924 −0.00773 3.63584 −1.30815 2.407824 3.63584 2.321528 −0.02999 3.63584 −1.36878 2.454192 3.63584 2.398164 −0.05051 3.63584 −1.42149 2.494304 3.63584 2.46468 −0.06817 3.63584 −1.46611 2.528068 3.63584 2.515832 −0.0816 3.63584 −1.50457 2.556588 3.63584 2.556864 −0.09218 3.63584 −1.5375 2.57968 3.63584 2.587592 −0.1001 3.63584 −1.56538 2.597436 3.63584 2.610868 −0.09807 3.63584 −1.58856 2.610316 3.63584 2.621816 −0.09062 3.63584 −1.60706 2.618688 3.63584 2.627152 −0.084 3.63584 −1.62159 2.623288 3.63584 2.629176 −0.08022 3.63584 −1.6342 2.625036 3.63584 2.630004 −0.07829 3.63584 −1.64422 2.62384 3.63584 −1.64662 2.70848 4.362824 2.584648 0.067436 4.362732 −1.65131 2.70204 4.362824 2.584924 0.068356 4.362732 −1.6537 2.691736 4.362824 2.585568 0.070288 4.362824 −1.65315 2.67858 4.362732 2.586396 0.074152 4.362824 −1.64993 2.663216 4.362824 2.586672 0.082156 4.362824 −1.6434 2.643252 4.362732 2.583452 0.094116 4.362732 −1.63272 2.618136 4.362824 2.568088 0.110032 4.362824 −1.61745 2.587868 4.362824 2.540948 0.123188 4.362732 −1.59712 2.55208 4.362732 2.504884 0.140668 4.362824 −1.57145 2.510404 4.362732 2.459712 0.162656 4.362824 −1.54036 2.462196 4.362732 2.4012 0.19136 4.362824 −1.50245 2.405984 4.362732 2.333764 0.224848 4.362824 −1.45746 2.342136 4.362732 2.261912 0.260636 4.362732 −1.40493 2.27102 4.362732 2.180952 0.300748 4.362732 −1.34504 2.192544 4.362732 2.091068 0.345552 4.362824 −1.27779 2.106708 4.362824 1.992812 0.395692 4.362824 −1.20106 2.015168 4.362824 1.890508 0.449144 4.362824 −1.11752 1.922616 4.362824 1.784248 0.505816 4.362732 −1.0281 1.828224 4.362732 1.67394 0.565708 4.362824 −0.93251 1.732084 4.362824 1.559768 0.62882 4.362824 −0.83076 1.635576 4.362732 1.441732 0.695336 4.362824 −0.72266 1.539068 4.362732 1.320016 0.765348 4.362824 −0.6083 1.442652 4.362824 1.194528 0.838856 4.362732 −0.48751 1.346236 4.362732 1.06536 0.916044 4.362824 −0.36441 1.253316 4.362732 0.936836 0.994336 4.362824 −0.23874 1.163984 4.362732 0.808864 1.073456 4.362824 −0.11068 1.077964 4.362824 0.681352 1.153312 4.362732 0.019964 0.995716 4.362824 0.554208 1.233812 4.362824 0.15364 0.9177 4.362824 0.42734 1.314772 4.362824 0.289892 0.843456 4.362824 0.300564 1.395916 4.362824 0.42872 0.7728 4.362824 0.173696 1.476876 4.362732 0.569756 0.70564 4.362824 0.047012 1.558204 4.362732 0.712264 0.641884 4.362824 −0.07912 1.64036 4.362824 0.856152 0.581164 4.362824 −0.2047 1.723344 4.362824 1.001144 0.523388 4.362824 −0.32964 1.807248 4.362732 1.142364 0.470028 4.362732 −0.4497 1.889404 4.362824 1.279628 0.420624 4.362824 −0.56516 1.969352 4.362824 1.412568 0.3749 4.362824 −0.67629 2.046908 4.362732 1.541092 0.332396 4.362824 −0.78292 2.12198 4.362732 1.665108 0.292928 4.362824 −0.88476 2.19512 4.362824 1.784616 0.256312 4.362824 −0.9821 2.266052 4.362824 1.899432 0.221996 4.362824 −1.07594 2.333212 4.362824 2.009372 0.189888 4.362732 −1.16159 2.394484 4.362732 2.109376 0.160816 4.362824 −1.23832 2.451064 4.362824 2.199628 0.135332 4.362824 −1.30668 2.502124 4.362824 2.280036 0.113712 4.362732 −1.36694 2.547112 4.362732 2.35566 0.09384 4.362824 −1.41928 2.58612 4.362824 2.421164 0.076728 4.362732 −1.46363 2.618872 4.362824 2.47158 0.063756 4.362824 −1.5019 2.646472 4.362824 2.511968 0.053452 4.362732 −1.53456 2.66892 4.362824 2.542236 0.045816 4.362824 −1.56225 2.686216 4.362824 2.565236 0.047104 4.362824 −1.58507 2.698728 4.362824 2.576184 0.05428 4.362824 −1.60347 2.706824 4.362732 2.581428 0.060812 4.362824 −1.61773 2.711424 4.362824 2.583452 0.064492 4.362732 −1.63015 2.713264 4.362824 2.58428 0.066424 4.362824 −1.64008 2.712068 4.362732 −1.63144 2.718968 5.089716 2.533312 0.11868 5.089716 −1.63594 2.712528 5.089716 2.53368 0.1196 5.089716 −1.63815 2.702408 5.089716 2.534232 0.121532 5.089716 −1.63751 2.689436 5.089716 2.534968 0.125304 5.089716 −1.63429 2.674256 5.089716 2.535152 0.133216 5.089716 −1.62785 2.654752 5.089716 2.531748 0.144992 5.089716 −1.61736 2.630004 5.089716 2.516292 0.160172 5.089716 −1.60227 2.600104 5.089716 2.489612 0.173144 5.089716 −1.58231 2.564868 5.089716 2.4541 0.19044 5.089716 −1.55701 2.523744 5.089716 2.409664 0.21206 5.089716 −1.52637 2.476364 5.089716 2.352072 0.240396 5.089716 −1.48911 2.420888 5.089716 2.28574 0.273424 5.089716 −1.44477 2.35796 5.089716 2.215084 0.308844 5.089716 −1.39316 2.287856 5.089716 2.135688 0.348772 5.089716 −1.33428 2.210576 5.089716 2.047644 0.393484 5.089716 −1.26804 2.125936 5.089716 1.951044 0.44344 5.089716 −1.19278 2.035592 5.089716 1.85058 0.49634 5.089716 −1.11072 1.944328 5.089716 1.74616 0.552368 5.089716 −1.02295 1.851224 5.089716 1.637784 0.611616 5.089716 −0.92938 1.75628 5.089716 1.525544 0.674084 5.089716 −0.82938 1.6606 5.089716 1.409624 0.739864 5.089716 −0.72312 1.565104 5.089716 1.290024 0.809048 5.089716 −0.6106 1.4697 5.089716 1.166744 0.88182 5.089716 −0.49192 1.374296 5.089716 1.039876 0.95818 5.089716 −0.37085 1.282388 5.089716 0.91356 1.03546 5.089716 −0.24739 1.19416 5.089716 0.787796 1.11366 5.089716 −0.12153 1.109244 5.089716 0.662492 1.192596 5.089716 0.0069 1.0281 5.089716 0.537556 1.272084 5.089716 0.138184 0.951096 5.089716 0.412712 1.35194 5.089716 0.272136 0.878048 5.089716 0.288052 1.431888 5.089716 0.408572 0.808496 5.089716 0.1633 1.511836 5.089716 0.547308 0.74244 5.089716 0.038732 1.591876 5.089716 0.687792 0.679604 5.089716 −0.08538 1.672836 5.089716 0.829472 0.619988 5.089716 −0.20902 1.75444 5.089716 0.972348 0.563224 5.089716 −0.33203 1.836964 5.089716 1.111544 0.510968 5.089716 −0.45025 1.91774 5.089716 1.246692 0.462576 5.089716 −0.56396 1.9964 5.089716 1.3777 0.417772 5.089716 −0.67335 2.072484 5.089716 1.504384 0.37628 5.089716 −0.7786 2.146084 5.089716 1.626744 0.337732 5.089716 −0.87897 2.217844 5.089716 1.744504 0.301944 5.089716 −0.97492 2.287396 5.089716 1.857664 0.268548 5.089716 −1.06748 2.353176 5.089716 1.96604 0.237452 5.089716 −1.15202 2.41316 5.089716 2.064848 0.209668 5.089716 −1.22783 2.468452 5.089716 2.153904 0.185288 5.089716 −1.29536 2.518316 5.089716 2.233208 0.16422 5.089716 −1.35498 2.562292 5.089716 2.307636 0.144808 5.089716 −1.40677 2.600288 5.089716 2.37222 0.128248 5.089716 −1.45066 2.632212 5.089716 2.4219 0.115552 5.089716 −1.48847 2.659076 5.089716 2.461736 0.105524 5.089716 −1.52085 2.68088 5.089716 2.491544 0.098072 5.089716 −1.54818 2.697716 5.089716 2.514176 0.098808 5.089716 −1.57081 2.709768 5.089716 2.525032 0.1058 5.089716 −1.58893 2.71768 5.089716 2.530184 0.112148 5.089716 −1.60301 2.722096 5.089716 2.532116 0.115828 5.089716 −1.61524 2.723844 5.089716 2.532944 0.117668 5.089716 −1.625 2.722556 5.089716 −1.60816 2.655672 5.816608 2.479768 0.100464 5.816608 −1.61258 2.649416 5.816608 2.480044 0.101384 5.816608 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10.17805 −1.34421 1.700804 10.17814 2.155928 −0.76259 10.17814 −1.36344 1.713224 10.17814 2.166048 −0.75753 10.17814 −1.3789 1.721596 10.17814 2.170832 −0.75192 10.17814 −1.39104 1.726656 10.17814 2.17258 −0.7487 10.17814 −1.40171 1.729324 10.17814 2.173224 −0.74695 10.17805 −1.41045 1.72914 10.17814 −1.39122 1.69142 10.54154 2.117472 −0.82515 10.54154 −1.395 1.685716 10.54154 2.117748 −0.82432 10.54154 −1.39619 1.676792 10.54154 2.118116 −0.82257 10.54154 −1.3949 1.665568 10.54154 2.118484 −0.81908 10.54154 −1.3915 1.652504 10.54154 2.11784 −0.81227 10.54154 −1.38515 1.635668 10.54154 2.11324 −0.80252 10.54154 −1.37531 1.614508 10.54154 2.097048 −0.79212 10.54154 −1.36142 1.589024 10.54154 2.07276 −0.78228 10.54154 −1.34302 1.55894 10.54154 2.040468 −0.76912 10.54154 −1.31956 1.52398 10.54154 2.00008 −0.75247 10.54154 −1.29104 1.483776 10.54154 1.947732 −0.73057 10.54154 −1.25672 1.436856 10.54154 1.887472 −0.7049 10.54154 −1.2167 1.382944 10.54154 1.823532 −0.67703 10.54154 −1.17088 1.322224 10.54154 1.751864 −0.64474 10.54154 −1.1189 1.25488 10.54154 1.672652 −0.6083 10.54154 −1.0603 1.181372 10.54154 1.585712 −0.56755 10.54154 −0.99507 1.1017 10.54154 1.495736 −0.5233 10.54154 −0.92552 1.020004 10.54154 1.402724 −0.47509 10.54154 −0.85174 0.936468 10.54154 1.306492 −0.42348 10.54154 −0.77372 0.851 10.54154 1.207408 −0.36837 10.54154 −0.69129 0.76406 10.54154 1.105564 −0.30949 10.54154 −0.60416 0.67574 10.54154 1.00096 −0.24684 10.54154 −0.51216 0.586408 10.54154 0.893688 −0.18014 10.54154 −0.41501 0.496248 10.54154 0.78384 −0.10948 10.54154 −0.31593 0.40848 10.54154 0.675096 −0.03717 10.54154 −0.21482 0.32292 10.54154 0.567456 0.036892 10.54154 −0.11187 0.239568 10.54154 0.460644 0.112424 10.54154 −0.00699 0.158608 10.54154 0.354936 0.18952 10.54154 0.100096 0.080132 10.54154 0.25024 0.268088 10.54154 0.209576 0.004508 10.54154 0.14628 0.347668 10.54154 0.321172 −0.06863 10.54154 0.043148 0.428352 10.54154 0.434792 −0.13929 10.54154 −0.05897 0.510232 10.54154 0.55062 −0.20755 10.54154 −0.15999 0.593492 10.54154 0.668012 −0.27324 10.54154 −0.26008 0.677948 10.54154 0.786692 −0.33635 10.54154 −0.35908 0.763508 10.54154 0.902704 −0.39486 10.54154 −0.45393 0.84732 10.54154 1.015956 −0.44914 10.54154 −0.54464 0.929108 10.54154 1.126172 −0.49938 10.54154 −0.63149 1.00878 10.54154 1.233076 −0.54584 10.54154 −0.71456 1.08606 10.54154 1.33676 −0.58852 10.54154 −0.79405 1.160764 10.54154 1.43704 −0.62772 10.54154 −0.87004 1.2328 10.54154 1.533548 −0.66424 10.54154 −0.94254 1.302168 10.54154 1.626192 −0.69819 10.54154 −1.00869 1.365648 10.54154 1.711016 −0.72744 10.54154 −1.0683 1.423332 10.54154 1.787836 −0.75238 10.54154 −1.12148 1.475036 10.54154 1.856284 −0.77381 10.54154 −1.16812 1.520944 10.54154 1.920684 −0.79332 10.54154 −1.20842 1.560872 10.54154 1.976712 −0.80978 10.54154 −1.24274 1.594452 10.54154 2.019768 −0.82211 10.54154 −1.27264 1.622512 10.54154 2.05436 −0.83177 10.54154 −1.29858 1.645236 10.54154 2.080304 −0.83895 10.54154 −1.32075 1.6629 10.54154 2.100176 −0.84152 10.54154 −1.33934 1.675964 10.54154 2.110204 −0.83646 10.54154 −1.35433 1.684888 10.54154 2.114896 −0.83094 10.54154 −1.36611 1.6905 10.54154 2.116552 −0.82772 10.54154 −1.3766 1.693628 10.54154 2.117196 −0.82598 10.54154 −1.38524 1.693996 10.54154 −1.36427 1.678724 10.90504 2.04746 −0.89626 10.90504 −1.36804 1.673204 10.90504 2.047644 −0.89544 10.90504 −1.36924 1.664372 10.90504 2.048012 −0.89378 10.90504 −1.36795 1.65324 10.90504 2.04838 −0.89028 10.90504 −1.36464 1.640268 10.90504 2.047644 −0.88348 10.90504 −1.35856 1.623524 10.90504 2.043044 −0.87382 10.90504 −1.34909 1.602456 10.90504 2.02676 −0.8636 10.90504 −1.33584 1.576972 10.90504 2.002656 −0.85404 10.90504 −1.31818 1.546796 10.90504 1.970548 −0.84116 10.90504 −1.29573 1.51156 10.90504 1.930528 −0.82478 10.90504 −1.2684 1.471172 10.90504 1.87864 −0.80325 10.90504 −1.23547 1.423884 10.90504 1.819024 −0.77786 10.90504 −1.1971 1.369604 10.90504 1.755636 −0.75017 10.90504 −1.15304 1.308424 10.90504 1.684796 −0.71806 10.90504 −1.10317 1.24062 10.90504 1.606596 −0.68135 10.90504 −1.04696 1.166376 10.90504 1.521128 −0.63977 10.90504 −0.9844 1.085876 10.90504 1.432624 −0.59469 10.90504 −0.91788 1.003168 10.90504 1.341176 −0.54565 10.90504 −0.84732 0.918436 10.90504 1.246876 −0.49284 10.90504 −0.77262 0.831588 10.90504 1.149816 −0.43636 10.90504 −0.69368 0.743084 10.90504 1.050088 −0.37573 10.90504 −0.61014 0.653016 10.90504 0.947784 −0.31114 10.90504 −0.52182 0.561752 10.90504 0.842904 −0.24242 10.90504 −0.42854 0.469384 10.90504 0.735632 −0.16965 10.90504 −0.33313 0.379408 10.90504 0.629372 −0.09531 10.90504 −0.2357 0.291548 10.90504 0.524216 −0.01941 10.90504 −0.13625 0.205896 10.90504 0.420072 0.057776 10.90504 −0.03468 0.122544 10.90504 0.317032 0.136436 10.90504 0.069 0.041584 10.90504 0.214912 0.216476 10.90504 0.17526 −0.03671 10.90504 0.113804 0.29762 10.90504 0.28382 −0.11242 10.90504 0.013708 0.380144 10.90504 0.394588 −0.18566 10.90504 −0.08519 0.463956 10.90504 0.507472 −0.25659 10.90504 −0.18299 0.549148 10.90504 0.62192 −0.32494 10.90504 −0.27959 0.635628 10.90504 0.737748 −0.39082 10.90504 −0.37508 0.723396 10.90504 0.851092 −0.45209 10.90504 −0.46626 0.809324 10.90504 0.961676 −0.50904 10.90504 −0.55347 0.89332 10.90504 1.0695 −0.56175 10.90504 −0.63673 0.975016 10.90504 1.17438 −0.61042 10.90504 −0.71631 1.054412 10.90504 1.27604 −0.65513 10.90504 −0.7924 1.131232 10.90504 1.374572 −0.69607 10.90504 −0.86498 1.205292 10.90504 1.4697 −0.7337 10.90504 −0.93426 1.276684 10.90504 1.56124 −0.76811 10.90504 −0.99728 1.342004 10.90504 1.645052 −0.79782 10.90504 −1.05423 1.401252 10.90504 1.721044 −0.82312 10.90504 −1.10492 1.454428 10.90504 1.788756 −0.84474 10.90504 −1.14954 1.501532 10.90504 1.852604 −0.86434 10.90504 −1.188 1.542472 10.90504 1.907988 −0.88072 10.90504 −1.22084 1.57688 10.90504 1.950676 −0.89304 10.90504 −1.24954 1.605676 10.90504 1.984992 −0.9028 10.90504 −1.27438 1.629044 10.90504 2.01066 −0.90997 10.90504 −1.29573 1.647352 10.90504 2.030348 −0.91255 10.90504 −1.31358 1.660968 10.90504 2.040284 −0.90758 10.90504 −1.32802 1.670444 10.90504 2.044884 −0.90206 10.90504 −1.33952 1.676516 10.90504 2.04654 −0.89884 10.90504 −1.34964 1.680104 10.90504 2.047184 −0.89718 10.90504 −1.3582 1.681024 10.90504 −1.33529 1.687004 11.26844 1.973584 −0.96536 11.26844 −1.33906 1.681576 11.26844 1.97386 −0.96453 11.26844 −1.34044 1.672744 11.26844 1.974136 −0.96278 11.26844 −1.33934 1.661704 11.26844 1.974504 −0.95938 11.26844 −1.3363 1.648824 11.26844 1.973768 −0.95257 11.26844 −1.33078 1.631988 11.26844 1.969076 −0.943 11.26844 −1.32195 1.610828 11.26844 1.952884 −0.93297 11.26844 −1.30962 1.58516 11.26844 1.928872 −0.92359 11.26844 −1.29306 1.554616 11.26844 1.896856 −0.91098 11.26844 −1.2719 1.51892 11.26844 1.85702 −0.89488 11.26844 −1.24614 1.477888 11.26844 1.8055 −0.87354 11.26844 −1.21504 1.429956 11.26844 1.74616 −0.84824 11.26844 −1.17861 1.374848 11.26844 1.683324 −0.82055 11.26844 −1.13675 1.31284 11.26844 1.613128 −0.78844 11.26844 −1.08928 1.244024 11.26844 1.535848 −0.75118 11.26844 −1.03592 1.168584 11.26844 1.45176 −0.70831 11.26844 −0.97658 1.086612 11.26844 1.364728 −0.66176 11.26844 −0.91338 1.002248 11.26844 1.274752 −0.61143 11.26844 −0.84631 0.915676 11.26844 1.182292 −0.55697 11.26844 −0.77538 0.826896 11.26844 1.08744 −0.49827 11.26844 −0.70012 0.736184 11.26844 0.990196 −0.43525 11.26844 −0.62045 0.643816 11.26844 0.890652 −0.368 11.26844 −0.53608 0.549884 11.26844 0.788716 −0.29642 11.26844 −0.44675 0.454848 11.26844 0.68448 −0.22071 11.26844 −0.3553 0.361928 11.26844 0.58144 −0.14361 11.26844 −0.26156 0.271216 11.26844 0.47932 −0.06504 11.26844 −0.16569 0.182712 11.26844 0.378212 0.014812 11.26844 −0.06753 0.096416 11.26844 0.278116 0.095772 11.26844 0.033028 0.012512 11.26844 0.179032 0.17802 11.26844 0.13616 −0.06882 11.26844 0.08096 0.261464 11.26844 0.241776 −0.14757 11.26844 −0.01592 0.34638 11.26844 0.349784 −0.22402 11.26844 −0.11141 0.43286 11.26844 0.459724 −0.29799 11.26844 −0.20562 0.52072 11.26844 0.571044 −0.36956 11.26844 −0.29854 0.60996 11.26844 0.683836 −0.43884 11.26844 −0.39026 0.700396 11.26844 0.794328 −0.50352 11.26844 −0.47766 0.788992 11.26844 0.902336 −0.56378 11.26844 −0.56111 0.875564 11.26844 1.007676 −0.61962 11.26844 −0.64078 0.959836 11.26844 1.110256 −0.67105 11.26844 −0.71668 1.041624 11.26844 1.210076 −0.71824 11.26844 −0.78918 1.120836 11.26844 1.306952 −0.7613 11.26844 −0.85827 1.197288 11.26844 1.400792 −0.80022 11.26844 −0.92405 1.27098 11.26844 1.491504 −0.83518 11.26844 −0.98394 1.338416 11.26844 1.574488 −0.86535 11.26844 −1.03804 1.399504 11.26844 1.649744 −0.8912 11.26844 −1.08624 1.454244 11.26844 1.716904 −0.91319 11.26844 −1.12866 1.502728 11.26844 1.7802 −0.93288 11.26844 −1.16536 1.544772 11.26844 1.835216 −0.94944 11.26844 −1.19674 1.5801 11.26844 1.877628 −0.96177 11.26844 −1.22415 1.609724 11.26844 1.911576 −0.97152 11.26844 −1.24807 1.633828 11.26844 1.93706 −0.97879 11.26844 −1.26859 1.652688 11.26844 1.956656 −0.98146 11.26844 −1.28579 1.666948 11.26844 1.9665 −0.97649 11.26844 −1.29978 1.676976 11.26844 1.9711 −0.97106 11.26844 −1.31082 1.683508 11.26844 1.972756 −0.96784 11.26844 −1.32075 1.687556 11.26844 1.973308 −0.96618 11.26844 −1.32922 1.688936 11.26844 −1.30502 1.70798 11.63193 1.899892 −1.03436 11.63193 −1.30898 1.702644 11.63193 1.900076 −1.03353 11.63193 −1.31045 1.693904 11.63193 1.900444 −1.03178 11.63193 −1.30971 1.682864 11.63193 1.900812 −1.02838 11.63193 −1.30714 1.669892 11.63193 1.899984 −1.02157 11.63193 −1.30217 1.653056 11.63193 1.8952 −1.01209 11.63193 −1.29416 1.63162 11.63193 1.878824 −1.00225 11.63193 −1.28276 1.605584 11.63193 1.854812 −0.99314 11.63193 −1.26748 1.574488 11.63193 1.82298 −0.98063 11.63193 −1.24789 1.538148 11.63193 1.783236 −0.9648 11.63193 −1.22388 1.49638 11.63193 1.731716 −0.94355 11.63193 −1.19462 1.447436 11.63193 1.672744 −0.91825 11.63193 −1.16049 1.391224 11.63193 1.610184 −0.89047 11.63193 −1.12111 1.327836 11.63193 1.540448 −0.85799 11.63193 −1.07649 1.257548 11.63193 1.463904 −0.82009 11.63193 −1.02617 1.18036 11.63193 1.38092 −0.77602 11.63193 −0.97023 1.096456 11.63193 1.295084 −0.728 11.63193 −0.91062 1.010068 11.63193 1.206488 −0.67611 11.63193 −0.84723 0.921196 11.63193 1.115592 −0.6198 11.63193 −0.78007 0.830024 11.63193 1.022764 −0.55881 11.63193 −0.70877 0.736644 11.63193 0.927912 −0.49312 11.63193 −0.63305 0.641516 11.63193 0.831036 −0.42292 11.63193 −0.55283 0.54464 11.63193 0.732136 −0.34813 11.63193 −0.46764 0.446384 11.63193 0.63112 −0.26901 11.63193 −0.38014 0.350244 11.63193 0.5313 −0.18842 11.63193 −0.29035 0.25622 11.63193 0.432492 −0.10663 11.63193 −0.19808 0.164496 11.63193 0.334604 −0.02364 11.63193 −0.10332 0.075072 11.63193 0.237636 0.060352 11.63193 −0.00598 −0.01196 11.63193 0.141588 0.14536 11.63193 0.094116 −0.0966 11.63193 0.046644 0.231656 11.63193 0.196788 −0.17876 11.63193 −0.04674 0.319608 11.63193 0.302036 −0.25861 11.63193 −0.13864 0.409216 11.63193 0.40894 −0.33608 11.63193 −0.22908 0.500204 11.63193 0.517316 −0.41133 11.63193 −0.31814 0.592664 11.63193 0.627256 −0.48447 11.63193 −0.40581 0.68632 11.63193 0.734988 −0.55301 11.63193 −0.48935 0.777952 11.63193 0.84042 −0.61686 11.63193 −0.56893 0.867376 11.63193 0.94346 −0.67602 11.63193 −0.64474 0.954592 11.63193 1.044016 −0.7303 11.63193 −0.71686 1.039232 11.63193 1.142088 −0.77998 11.63193 −0.7855 1.121204 11.63193 1.237492 −0.82524 11.63193 −0.85091 1.200324 11.63193 1.330412 −0.86572 11.63193 −0.9131 1.276592 11.63193 1.42048 −0.90169 11.63193 −0.96968 1.346328 11.63193 1.503004 −0.9327 11.63193 −1.02074 1.409624 11.63193 1.577708 −0.95938 11.63193 −1.06628 1.466296 11.63193 1.644592 −0.98182 11.63193 −1.10648 1.516344 11.63193 1.707704 −1.00188 11.63193 −1.14126 1.559676 11.63193 1.762536 −1.01853 11.63193 −1.17116 1.596016 11.63193 1.804856 −1.03095 11.63193 −1.19738 1.626468 11.63193 1.838712 −1.0407 11.63193 −1.22029 1.651308 11.63193 1.864196 −1.04797 11.63193 −1.23998 1.670996 11.63193 1.883424 −1.05027 11.63193 −1.25654 1.685808 11.63193 1.892992 −1.0453 11.63193 −1.27006 1.696296 11.63193 1.897408 −1.03997 11.63193 −1.28082 1.703288 11.63193 1.898972 −1.03684 11.63193 −1.29048 1.707888 11.63193 1.899616 −1.03518 11.63193 −1.29886 1.709544 11.63193 −1.22967 1.76502 12.51145 1.721872 −1.20134 12.51145 −1.2339 1.760052 12.51145 1.722148 −1.20051 12.51145 −1.23593 1.751404 12.51145 1.722516 −1.19885 12.51145 −1.23602 1.740364 12.51145 1.722884 −1.19536 12.51145 −1.23446 1.727208 12.51145 1.722056 −1.18855 12.51145 −1.23096 1.709912 12.51145 1.716904 −1.17916 12.51145 −1.22507 1.687924 12.51145 1.700252 −1.16987 12.51145 −1.21615 1.660876 12.51145 1.676148 −1.16113 12.51145 −1.204 1.628492 12.51145 1.644132 −1.14917 12.51145 −1.18809 1.590404 12.51145 1.604388 −1.13372 12.51145 −1.16831 1.546428 12.51145 1.553052 −1.11265 12.51145 −1.14402 1.494908 12.51145 1.494356 −1.08716 12.51145 −1.11578 1.435568 12.51145 1.43244 −1.05864 12.51145 −1.0833 1.368408 12.51145 1.363808 −1.02479 12.51145 −1.04659 1.293704 12.51145 1.288644 −0.98495 12.51145 −1.00409 1.212008 12.51145 1.207592 −0.93812 12.51145 −0.95652 1.123044 12.51145 1.124148 −0.8867 12.51145 −0.90565 1.031228 12.51145 1.038588 −0.83058 12.51145 −0.85118 0.936652 12.51145 0.951372 −0.76949 12.51145 −0.79313 0.8395 12.51145 0.862776 −0.70316 12.51145 −0.73103 0.739956 12.51145 0.772708 −0.63158 12.51145 −0.66479 0.638204 12.51145 0.681352 −0.55485 12.51145 −0.59423 0.534428 12.51145 0.588708 −0.47297 12.51145 −0.51897 0.428812 12.51145 0.49496 −0.38603 12.51145 −0.44123 0.325128 12.51145 0.402868 −0.29734 12.51145 −0.36092 0.223652 12.51145 0.312248 −0.20709 12.51145 −0.27766 0.124292 12.51145 0.222916 −0.11564 12.51145 −0.19164 0.027324 12.51145 0.134504 −0.02328 12.51145 −0.10286 −0.06753 12.51145 0.047012 0.070104 12.51145 −0.01122 −0.16017 12.51145 −0.0391 0.16468 12.51145 0.083168 −0.25052 12.51145 −0.12337 0.26082 12.51145 0.180228 −0.33874 12.51145 −0.2058 0.358524 12.51145 0.279588 −0.42522 12.51145 −0.28649 0.4577 12.51145 0.38088 −0.50977 12.51145 −0.36561 0.558164 12.51145 0.484012 −0.59202 12.51145 −0.44326 0.659732 12.51145 0.585488 −0.66902 12.51145 −0.51704 0.758908 12.51145 0.685492 −0.74078 12.51145 −0.58705 0.8556 12.51145 0.78384 −0.80739 12.51145 −0.65338 0.949624 12.51145 0.88044 −0.86848 12.51145 −0.71631 1.040888 12.51145 0.974832 −0.92442 12.51145 −0.77593 1.129208 12.51145 1.0672 −0.9752 12.51145 −0.83251 1.214492 12.51145 1.157452 −1.02065 12.51145 −0.88624 1.296556 12.51145 1.245496 −1.06122 12.51145 −0.93481 1.37172 12.51145 1.326456 −1.09581 12.51145 −0.97796 1.44026 12.51145 1.400148 −1.12479 12.51145 −1.01688 1.50144 12.51145 1.46648 −1.1488 12.51145 −1.05147 1.55526 12.51145 1.529132 −1.16978 12.51145 −1.08192 1.601536 12.51145 1.583872 −1.1868 12.51145 −1.10814 1.64036 12.51145 1.6261 −1.19922 12.51145 −1.13132 1.673112 12.51145 1.660048 −1.2087 12.51145 −1.15166 1.699976 12.51145 1.685624 −1.2156 12.51145 −1.16923 1.72132 12.51145 1.705036 −1.21725 12.51145 −1.18422 1.737788 12.51145 1.714696 −1.21219 12.51145 −1.19646 1.749656 12.51145 1.719296 −1.20686 12.51145 −1.2063 1.757752 12.51145 1.720952 −1.20382 12.51145 −1.21532 1.763364 12.51145 1.721596 −1.20216 12.51145 −1.22342 1.766032 12.51145

The coordinate values given in scalable TABLE 2 below provide the nominal profile for another exemplary stage compressor variable stator vane

TABLE 2 SUCTION SIDE PRESSURE SIDE X Y Z X Y Z 1.70721 −1.68519 −0.71432 −0.91026 1.11713 −0.71432 1.707557 −1.68449 −0.71432 −0.91599 1.114442 −0.71432 1.708163 −1.68311 −0.71432 −0.92266 1.109327 −0.71432 1.709204 −1.68016 −0.71432 −0.92951 1.101437 −0.71432 1.710678 −1.67426 −0.71432 −0.93567 1.090426 −0.71432 1.711285 −1.66464 −0.71432 −0.9413 1.074733 −0.71432 1.707036 −1.64808 −0.71432 −0.94538 1.053405 −0.71432 1.691344 −1.63152 −0.71432 −0.94694 1.026441 −0.71432 1.665854 −1.61392 −0.71432 −0.94529 0.993582 −0.71432 1.634122 −1.59164 −0.71432 −0.93983 0.955087 −0.71432 1.593113 −1.56225 −0.71432 −0.9309 0.91061 −0.71432 1.546208 −1.52783 −0.71432 −0.91859 0.858417 −0.71432 1.496529 −1.49055 −0.71432 −0.90272 0.798507 −0.71432 1.441388 −1.4478 −0.71432 −0.88261 0.731228 −0.71432 1.380958 −1.39934 −0.71432 −0.85781 0.657099 −0.71432 1.315412 −1.34498 −0.71432 −0.82825 0.576295 −0.71432 1.247873 −1.28706 −0.71432 −0.79296 0.489075 −0.71432 1.178513 −1.2255 −0.71432 −0.75316 0.3996 −0.71432 1.107159 −1.16013 −0.71432 −0.70869 0.307785 −0.71432 1.034071 −1.09112 −0.71432 −0.65909 0.213889 −0.71432 0.959249 −1.01812 −0.71432 −0.60421 0.117912 −0.71432 0.882606 −0.94139 −0.71432 −0.54396 0.020114 −0.71432 0.804316 −0.86084 −0.71432 −0.47798 −0.07942 −0.71432 0.724292 −0.77657 −0.71432 −0.40688 −0.17999 −0.71432 0.645048 −0.69152 −0.71432 −0.33319 −0.27805 −0.71432 0.566411 −0.60603 −0.71432 −0.25698 −0.37376 −0.71432 0.488121 −0.5202 −0.71432 −0.17808 −0.46697 −0.71432 0.409744 −0.43428 −0.71432 −0.09728 −0.55835 −0.71432 0.331194 −0.34871 −0.71432 −0.01413 −0.64756 −0.71432 0.25221 −0.26348 −0.71432 0.072221 −0.73366 −0.71432 0.1734 −0.17808 −0.71432 0.161782 −0.8168 −0.71432 0.095717 −0.09173 −0.71432 0.254291 −0.89708 −0.71432 0.018554 −0.00486 −0.71432 0.349488 −0.97494 −0.71432 −0.05792 0.082625 −0.71432 0.447112 −1.05046 −0.71432 −0.1336 0.170712 −0.71432 0.546904 −1.12355 −0.71432 −0.206 0.256632 −0.71432 0.645048 −1.19169 −0.71432 −0.27501 0.340211 −0.71432 0.741198 −1.25542 −0.71432 −0.34056 0.421622 −0.71432 0.835355 −1.31472 −0.71432 −0.40272 0.500779 −0.71432 0.927343 −1.36977 −0.71432 −0.46159 0.577682 −0.71432 1.016991 −1.42067 −0.71432 −0.51717 0.652157 −0.71432 1.104125 −1.46766 −0.71432 −0.56971 0.724118 −0.71432 1.18857 −1.51083 −0.71432 −0.61713 0.790271 −0.71432 1.270155 −1.55037 −0.71432 −0.6597 0.850267 −0.71432 1.345237 −1.58462 −0.71432 −0.69759 0.904108 −0.71432 1.413297 −1.61427 −0.71432 −0.73088 0.951793 −0.71432 1.474247 −1.63958 −0.71432 −0.75967 0.993149 −0.71432 1.531816 −1.66213 −0.71432 −0.78437 1.027742 −0.71432 1.582015 −1.68085 −0.71432 −0.80692 1.05644 −0.71432 1.620857 −1.69481 −0.71432 −0.82738 1.078982 −0.71432 1.652069 −1.70556 −0.71432 −0.84602 1.095975 −0.71432 1.676084 −1.70938 −0.71432 −0.8624 1.107593 −0.71432 1.692991 −1.70244 −0.71432 −0.87619 1.114702 −0.71432 1.700534 −1.69551 −0.71432 −0.88729 1.118257 −0.71432 1.704435 −1.69022 −0.71432 −0.89691 1.119384 −0.71432 1.706083 −1.68744 −0.71432 −0.90471 1.11869 −0.71432 1.706863 −1.68597 −0.71432 1.722642 −1.43809 0 −0.9159 1.037712 0 1.722989 −1.4374 0 −0.92084 1.034591 0 1.723509 −1.4361 0 −0.92648 1.029042 0 1.724463 −1.43332 0 −0.93185 1.020893 0 1.725764 −1.42769 0 −0.93627 1.010055 0 1.72585 −1.41867 0 −0.93965 0.994796 0 1.720735 −1.40333 0 −0.94113 0.974595 0 1.704956 −1.3885 0 −0.93974 0.949365 0 1.680853 −1.37194 0 −0.93489 0.91902 0 1.650855 −1.35113 0 −0.92622 0.883733 0 1.611926 −1.32382 0 −0.91373 0.843158 0 1.567276 −1.29218 0 −0.89735 0.795733 0 1.519851 −1.25802 0 −0.8768 0.741632 0 1.466877 −1.21909 0 −0.85183 0.680855 0 1.408615 −1.17505 0 −0.822 0.614009 0 1.345064 −1.12606 0 −0.78715 0.541355 0 1.279345 −1.07395 0 −0.7464 0.463325 0 1.211459 −1.01873 0 −0.70158 0.383387 0 1.141492 −0.9602 0 −0.65242 0.301629 0 1.069531 −0.89847 0 −0.59858 0.218224 0 0.995663 −0.83345 0 −0.53997 0.133431 0 0.9198 −0.76495 0 −0.47642 0.047165 0 0.841857 −0.69325 0 −0.40775 −0.04049 0 0.762006 −0.61826 0 −0.33388 −0.12918 0 0.682676 −0.54283 0 −0.25785 −0.21562 0 0.603605 −0.46705 0 −0.17973 −0.29964 0 0.524622 −0.39119 0 −0.09962 −0.38139 0 0.445465 −0.31541 0 −0.0176 −0.46098 0 0.366047 −0.24007 0 0.066412 −0.53815 0 0.28611 −0.16516 0 0.152852 −0.61245 0 0.206346 −0.09008 0 0.241806 −0.68389 0 0.127276 −0.01431 0 0.333015 −0.75282 0 0.048812 0.062164 0 0.426217 −0.8194 0 −0.02904 0.139154 0 0.521154 −0.88382 0 −0.10629 0.21675 0 0.617911 −0.94624 0 −0.18042 0.292352 0 0.712847 −1.00477 0 −0.25126 0.365961 0 0.80553 −1.05947 0 −0.31888 0.437662 0 0.896045 −1.11045 0 −0.3833 0.507368 0 0.984132 −1.15779 0 −0.4446 0.574994 0 1.069791 −1.20149 0 −0.50286 0.640453 0 1.15285 −1.2418 0 −0.55817 0.703657 0 1.233134 −1.27891 0 −0.60846 0.761573 0 1.310557 −1.31307 0 −0.65372 0.814113 0 1.381478 −1.3429 0 −0.69421 0.861191 0 1.445636 −1.36891 0 −0.72993 0.90272 0 1.502945 −1.39154 0 −0.76114 0.938441 0 1.556872 −1.41208 0 −0.7881 0.968179 0 1.603777 −1.42934 0 −0.81238 0.992542 0 1.640017 −1.44234 0 −0.83414 1.011442 0 1.669062 −1.45257 0 −0.85339 1.025141 0 1.691344 −1.45821 0 −0.87003 1.034244 0 1.70825 −1.45379 0 −0.88373 1.03936 0 1.715966 −1.44772 0 −0.89448 1.041354 0 1.719955 −1.44286 0 −0.90359 1.041354 0 1.721602 −1.44017 0 −0.91078 1.03988 0 1.722296 −1.43879 0 1.733133 −1.26799 0.490115 −0.91876 1.005373 0.490115 1.73348 −1.26738 0.490115 −0.92327 1.001905 0.490115 1.734 −1.26608 0.490115 −0.92812 0.996183 0.490115 1.734867 −1.26339 0.490115 −0.93255 0.98786 0.490115 1.735994 −1.25793 0.490115 −0.93575 0.977022 0.490115 1.735907 −1.24926 0.490115 −0.93766 0.96211 0.490115 1.730185 −1.23469 0.490115 −0.9374 0.942602 0.490115 1.714319 −1.22108 0.490115 −0.93419 0.918673 0.490115 1.690997 −1.2053 0.490115 −0.92752 0.889889 0.490115 1.661866 −1.18545 0.490115 −0.91694 0.856509 0.490115 1.624151 −1.15953 0.490115 −0.90246 0.818361 0.490115 1.580714 −1.12944 0.490115 −0.88365 0.773971 0.490115 1.53459 −1.09702 0.490115 −0.86024 0.723598 0.490115 1.482917 −1.06025 0.490115 −0.83215 0.667157 0.490115 1.425782 −1.01907 0.490115 −0.79903 0.604819 0.490115 1.363271 −0.97329 0.490115 −0.76062 0.53728 0.490115 1.298506 −0.92474 0.490115 −0.7164 0.464972 0.490115 1.231313 −0.8735 0.490115 −0.66837 0.39093 0.490115 1.161953 −0.81932 0.490115 −0.61626 0.315415 0.490115 1.090339 −0.76235 0.490115 −0.55974 0.238685 0.490115 1.016471 −0.70244 0.490115 −0.4987 0.160655 0.490115 0.940522 −0.63959 0.490115 −0.43324 0.081585 0.490115 0.862318 −0.57378 0.490115 −0.36301 0.001474 0.490115 0.781947 −0.50511 0.490115 −0.28802 −0.07968 0.490115 0.70201 −0.43601 0.490115 −0.21068 −0.15901 0.490115 0.622333 −0.36665 0.490115 −0.13126 −0.23634 0.490115 0.542829 −0.29703 0.490115 −0.05037 −0.3116 0.490115 0.463238 −0.2275 0.490115 0.032252 −0.38434 0.490115 0.383474 −0.15823 0.490115 0.116785 −0.45448 0.490115 0.303537 −0.08913 0.490115 0.203312 −0.52167 0.490115 0.223599 −0.02011 0.490115 0.291832 −0.58618 0.490115 0.143922 0.049332 0.490115 0.382174 −0.648 0.490115 0.064852 0.119473 0.490115 0.474076 −0.70756 0.490115 −0.01353 0.190307 0.490115 0.567625 −0.76487 0.490115 −0.09147 0.261661 0.490115 0.662475 −0.82027 0.490115 −0.16638 0.331107 0.490115 0.755504 −0.87203 0.490115 −0.23816 0.398733 0.490115 0.846365 −0.92049 0.490115 −0.30683 0.464452 0.490115 0.934973 −0.96584 0.490115 −0.37246 0.52835 0.490115 1.021066 −1.00806 0.490115 −0.43515 0.590254 0.490115 1.104385 −1.04734 0.490115 −0.49488 0.64999 0.490115 1.185016 −1.08392 0.490115 −0.55193 0.707559 0.490115 1.262699 −1.11791 0.490115 −0.60387 0.760272 0.490115 1.337521 −1.14938 0.490115 −0.65077 0.807957 0.490115 1.405841 −1.17721 0.490115 −0.69282 0.850614 0.490115 1.467571 −1.20149 0.490115 −0.72993 0.888155 0.490115 1.522712 −1.22256 0.490115 −0.76261 0.920321 0.490115 1.574559 −1.2418 0.490115 −0.79088 0.946764 0.490115 1.619556 −1.25828 0.490115 −0.81611 0.968266 0.490115 1.654323 −1.27068 0.490115 −0.83839 0.984825 0.490115 1.682153 −1.28056 0.490115 −0.8579 0.996703 0.490115 1.703308 −1.28645 0.490115 −0.87446 1.00442 0.490115 1.719434 −1.28264 0.490115 −0.88798 1.008581 0.490115 1.726804 −1.27709 0.490115 −0.89839 1.010055 0.490115 1.730619 −1.27258 0.490115 −0.90714 1.009622 0.490115 1.732179 −1.26998 0.490115 −0.91399 1.007714 0.490115 1.732873 −1.26868 0.490115 1.736774 −1.16421 0.774578 −0.91859 1.025488 0.774578 1.737035 −1.1636 0.774578 −0.92292 1.02202 0.774578 1.737555 −1.1623 0.774578 −0.92752 1.016211 0.774578 1.738508 −1.1597 0.774578 −0.9315 1.007801 0.774578 1.739549 −1.15432 0.774578 −0.93411 0.99705 0.774578 1.739289 −1.14574 0.774578 −0.93532 0.982224 0.774578 1.73322 −1.13152 0.774578 −0.93428 0.96315 0.774578 1.71718 −1.11852 0.774578 −0.93029 0.939741 0.774578 1.694118 −1.10308 0.774578 −0.92283 0.911651 0.774578 1.665334 −1.08366 0.774578 −0.91156 0.879225 0.774578 1.628053 −1.05835 0.774578 −0.8963 0.842117 0.774578 1.585136 −1.02896 0.774578 −0.87654 0.799114 0.774578 1.539532 −0.99731 0.774578 −0.852 0.750302 0.774578 1.488292 −0.96159 0.774578 −0.8227 0.695681 0.774578 1.431504 −0.92162 0.774578 −0.78845 0.635424 0.774578 1.369427 −0.87732 0.774578 −0.74883 0.570226 0.774578 1.304835 −0.8305 0.774578 −0.70348 0.500346 0.774578 1.237816 −0.78099 0.774578 −0.65432 0.428905 0.774578 1.168543 −0.72889 0.774578 −0.60118 0.356077 0.774578 1.096928 −0.67409 0.774578 −0.5437 0.282122 0.774578 1.022973 −0.61652 0.774578 −0.48188 0.206953 0.774578 0.946851 −0.55618 0.774578 −0.41564 0.130744 0.774578 0.868474 −0.49315 0.774578 −0.34481 0.053494 0.774578 0.787843 −0.42734 0.774578 −0.26929 −0.02454 0.774578 0.707559 −0.36102 0.774578 −0.19152 −0.10083 0.774578 0.627621 −0.29435 0.774578 −0.11193 −0.17513 0.774578 0.547857 −0.2275 0.774578 −0.03095 −0.24736 0.774578 0.468093 −0.16066 0.774578 0.05176 −0.31715 0.774578 0.388243 −0.0939 0.774578 0.136292 −0.38417 0.774578 0.308219 −0.02731 0.774578 0.222732 −0.44841 0.774578 0.228108 0.039275 0.774578 0.310993 −0.50997 0.774578 0.148344 0.106121 0.774578 0.400988 −0.56901 0.774578 0.069187 0.17366 0.774578 0.492543 −0.62571 0.774578 −0.00945 0.241893 0.774578 0.585485 −0.68033 0.774578 −0.08757 0.310733 0.774578 0.679728 −0.73305 0.774578 −0.16256 0.377665 0.774578 0.772064 −0.78221 0.774578 −0.23461 0.442864 0.774578 0.862232 −0.82816 0.774578 −0.30354 0.506241 0.774578 0.950059 −0.87116 0.774578 −0.36943 0.567798 0.774578 1.035198 −0.91139 0.774578 −0.43246 0.627448 0.774578 1.11765 −0.94893 0.774578 −0.49254 0.685017 0.774578 1.19724 −0.98396 0.774578 −0.55002 0.740418 0.774578 1.273883 −1.01664 0.774578 −0.60239 0.791138 0.774578 1.347578 −1.04716 0.774578 −0.64973 0.837002 0.774578 1.414857 −1.07421 0.774578 −0.69213 0.878011 0.774578 1.475547 −1.09797 0.774578 −0.72967 0.914078 0.774578 1.529822 −1.11843 0.774578 −0.76261 0.94477 0.774578 1.580801 −1.13733 0.774578 −0.79131 0.97 0.774578 1.625018 −1.15346 0.774578 −0.81671 0.990374 0.774578 1.659178 −1.16577 0.774578 −0.83917 1.006154 0.774578 1.686488 −1.17548 0.774578 −0.85859 1.017511 0.774578 1.70721 −1.18172 0.774578 −0.87498 1.024881 0.774578 1.723076 −1.17851 0.774578 −0.88833 1.028956 0.774578 1.730532 −1.17314 0.774578 −0.89865 1.030343 0.774578 1.73426 −1.16872 0.774578 −0.90723 1.029823 0.774578 1.735821 −1.1662 0.774578 −0.91399 1.027915 0.774578 1.736428 −1.1649 0.774578 1.735214 −1.05011 1.059041 −0.91763 1.068924 1.059041 1.735474 −1.0495 1.059041 −0.92188 1.06537 1.059041 1.735994 −1.0482 1.059041 −0.92622 1.059474 1.059041 1.736774 −1.04569 1.059041 −0.92977 1.051064 1.059041 1.737815 −1.04031 1.059041 −0.93203 1.0404 1.059041 1.737381 −1.03182 1.059041 −0.93272 1.025834 1.059041 1.731139 −1.01803 1.059041 −0.93107 1.007107 1.059041 1.715099 −1.00546 1.059041 −0.92656 0.984132 1.059041 1.692211 −0.99037 1.059041 −0.91859 0.956648 1.059041 1.663773 −0.97147 1.059041 −0.90671 0.924916 1.059041 1.626752 −0.94668 1.059041 −0.89093 0.888762 1.059041 1.584269 −0.91789 1.059041 −0.87055 0.846886 1.059041 1.539012 −0.88711 1.059041 −0.84533 0.799287 1.059041 1.488032 −0.85243 1.059041 −0.81533 0.74614 1.059041 1.43159 −0.81368 1.059041 −0.7803 0.687618 1.059041 1.369773 −0.77076 1.059041 −0.73998 0.62424 1.059041 1.305442 −0.72551 1.059041 −0.69386 0.556354 1.059041 1.238596 −0.67773 1.059041 −0.64409 0.487081 1.059041 1.16941 −0.62753 1.059041 −0.59025 0.41642 1.059041 1.097795 −0.57465 1.059041 −0.53225 0.344633 1.059041 1.023927 −0.51916 1.059041 −0.47 0.271718 1.059041 0.947718 −0.46107 1.059041 −0.40333 0.197936 1.059041 0.869254 −0.40029 1.059041 −0.33215 0.123201 1.059041 0.78845 −0.33692 1.059041 −0.25637 0.047685 1.059041 0.708079 −0.27302 1.059041 −0.17843 −0.02601 1.059041 0.628055 −0.20869 1.059041 −0.09875 −0.0978 1.059041 0.548117 −0.14418 1.059041 −0.01769 −0.16733 1.059041 0.468353 −0.07959 1.059041 0.065025 −0.23452 1.059041 0.388589 −0.015 1.059041 0.149471 −0.29903 1.059041 0.308565 0.049419 1.059041 0.235737 −0.36059 1.059041 0.228541 0.11375 1.059041 0.323825 −0.41954 1.059041 0.148864 0.178429 1.059041 0.413472 −0.47616 1.059041 0.069707 0.2438 1.059041 0.504507 −0.53043 1.059041 −0.00884 0.309866 1.059041 0.597016 −0.58262 1.059041 −0.08696 0.376538 1.059041 0.690652 −0.633 1.059041 −0.16204 0.441476 1.059041 0.782294 −0.67999 1.059041 −0.234 0.504681 1.059041 0.871682 −0.72395 1.059041 −0.30293 0.566238 1.059041 0.958729 −0.76513 1.059041 −0.36891 0.625974 1.059041 1.043174 −0.80354 1.059041 −0.43194 0.683803 1.059041 1.124672 −0.8396 1.059041 −0.49211 0.739724 1.059041 1.203396 −0.87342 1.059041 −0.54959 0.793478 1.059041 1.279085 −0.90506 1.059041 −0.60204 0.842551 1.059041 1.35174 −0.93463 1.059041 −0.64956 0.887028 1.059041 1.418065 −0.96098 1.059041 −0.69204 0.926736 1.059041 1.477888 −0.98422 1.059041 −0.72967 0.961676 1.059041 1.531382 −1.00425 1.059041 −0.7627 0.991501 1.059041 1.581581 −1.0228 1.059041 −0.79131 1.015951 1.059041 1.625105 −1.03867 1.059041 −0.81671 1.035718 1.059041 1.658658 −1.0508 1.059041 −0.83908 1.050891 1.059041 1.685535 −1.06051 1.059041 −0.85842 1.061902 1.059041 1.705909 −1.06684 1.059041 −0.87463 1.068924 1.059041 1.721602 −1.06407 1.059041 −0.88781 1.072652 1.059041 1.728971 −1.05895 1.059041 −0.89804 1.073953 1.059041 1.7327 −1.05453 1.059041 −0.90654 1.073346 1.059041 1.734173 −1.0521 1.059041 −0.91312 1.071352 1.059041 1.734867 −1.0508 1.059041 1.731486 −0.93506 1.343503 −0.91651 1.123719 1.343503 1.731833 −0.93445 1.343503 −0.92058 1.120164 1.343503 1.732266 −0.93324 1.343503 −0.92474 1.114268 1.343503 1.733133 −0.93064 1.343503 −0.92804 1.105859 1.343503 1.734 −0.92535 1.343503 −0.93003 1.095281 1.343503 1.733567 −0.91703 1.343503 −0.93029 1.080889 1.343503 1.727064 −0.9035 1.343503 −0.92821 1.062422 1.343503 1.710938 −0.89136 1.343503 −0.92327 1.03988 1.343503 1.688222 −0.87671 1.343503 −0.91477 1.012916 1.343503 1.659958 −0.85816 1.343503 −0.90255 0.981878 1.343503 1.623197 −0.83405 1.343503 −0.88633 0.946504 1.343503 1.580888 −0.80614 1.343503 −0.86544 0.905495 1.343503 1.535804 −0.77623 1.343503 −0.83978 0.859024 1.343503 1.485084 −0.74259 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0.519853 8.170435 1.284721 −0.94382 8.170435 −0.64227 0.467573 8.170435 1.224464 −0.91217 8.170435 −0.60621 0.410611 8.170435 1.161867 −0.8781 8.170435 −0.56528 0.349054 8.170435 1.097102 −0.8416 8.170435 −0.52124 0.285763 8.170435 1.030343 −0.80241 8.170435 −0.47382 0.220825 8.170435 0.961503 −0.76053 8.170435 −0.42318 0.154239 8.170435 0.890756 −0.71606 8.170435 −0.36952 0.08618 8.170435 0.818101 −0.66863 8.170435 −0.31255 0.016907 8.170435 0.743799 −0.61808 8.170435 −0.25186 −0.05323 8.170435 0.667937 −0.5645 8.170435 −0.18736 −0.12407 8.170435 0.592855 −0.5098 8.170435 −0.12086 −0.19291 8.170435 0.518639 −0.45387 8.170435 −0.05237 −0.25984 8.170435 0.445291 −0.39674 8.170435 0.018034 −0.32495 8.170435 0.37255 −0.33882 8.170435 0.090255 −0.38816 8.170435 0.300502 −0.28013 8.170435 0.16447 −0.44945 8.170435 0.229322 −0.22039 8.170435 0.240853 −0.50876 8.170435 0.159008 −0.15961 8.170435 0.319056 −0.56528 8.170435 0.089648 −0.09771 8.170435 0.398733 −0.61895 8.170435 0.021328 −0.03468 8.170435 0.479711 −0.67002 8.170435 −0.04586 0.029565 8.170435 0.561903 −0.71866 8.170435 −0.11184 0.09485 8.170435 0.645308 −0.76487 8.170435 −0.17444 0.159181 8.170435 0.727066 −0.80735 8.170435 −0.23418 0.221952 8.170435 0.806917 −0.84645 8.170435 −0.29123 0.282902 8.170435 0.884774 −0.88243 8.170435 −0.34567 0.342118 8.170435 0.960636 −0.91538 8.170435 −0.39769 0.399427 8.170435 1.034331 −0.94555 8.170435 −0.44711 0.454828 8.170435 1.105685 −0.97321 8.170435 −0.4941 0.508322 8.170435 1.174698 −0.99861 8.170435 −0.53676 0.557481 8.170435 1.241111 −1.02193 8.170435 −0.57543 0.601698 8.170435 1.301974 −1.04231 8.170435 −0.61028 0.641233 8.170435 1.357115 −1.05982 8.170435 −0.64097 0.676 8.170435 1.406274 −1.07482 8.170435 −0.66768 0.706172 8.170435 1.452572 −1.08843 8.170435 −0.69048 0.731488 8.170435 1.492714 −1.09979 8.170435 −0.71042 0.752643 8.170435 1.523753 −1.10829 8.170435 −0.72793 0.769809 8.170435 1.548549 −1.11505 8.170435 −0.74293 0.783161 8.170435 1.567189 −1.11999 8.170435 −0.75568 0.792958 8.170435 1.581495 −1.1212 8.170435 −0.76608 0.799721 8.170435 1.588691 −1.11756 8.170435 −0.7744 0.803796 8.170435 1.592159 −1.11366 8.170435 −0.78177 0.80605 8.170435 1.593459 −1.11141 8.170435 −0.78802 0.806223 8.170435 1.594066 −1.11028 8.170435 1.577593 −1.2053 8.454897 −0.78429 0.83154 8.454897 1.577767 −1.2047 8.454897 −0.78776 0.827985 8.454897 1.578113 −1.20348 8.454897 −0.7901 0.821743 8.454897 1.578547 −1.20097 8.454897 −0.79088 0.813419 8.454897 1.578374 −1.19594 8.454897 −0.79036 0.803449 8.454897 1.575252 −1.18866 8.454897 −0.78819 0.790444 8.454897 1.563721 −1.18068 8.454897 −0.78403 0.773711 8.454897 1.546381 −1.17288 8.454897 −0.77753 0.753336 8.454897 1.523406 −1.1623 8.454897 −0.76834 0.728974 8.454897 1.494708 −1.14904 8.454897 −0.75628 0.700536 8.454897 1.457514 −1.13152 8.454897 −0.7412 0.66759 8.454897 1.414771 −1.11089 8.454897 −0.72273 0.628922 8.454897 1.369427 −1.08852 8.454897 −0.7008 0.584705 8.454897 1.318707 −1.06268 8.454897 −0.67531 0.534939 8.454897 1.262786 −1.0332 8.454897 −0.64565 0.479971 8.454897 1.201835 −0.99982 8.454897 −0.6115 0.419975 8.454897 1.138718 −0.96376 8.454897 −0.57274 0.355123 8.454897 1.073519 −0.92492 8.454897 −0.53086 0.288191 8.454897 1.006327 −0.88313 8.454897 −0.48561 0.219438 8.454897 0.9374 −0.83839 8.454897 −0.43714 0.148951 8.454897 0.866567 −0.79079 8.454897 −0.38564 0.076816 8.454897 0.794085 −0.73998 8.454897 −0.33067 0.003295 8.454897 0.719957 −0.68588 8.454897 −0.27206 −0.07118 8.454897 0.644441 −0.62858 8.454897 −0.20938 −0.14661 8.454897 0.569792 −0.56997 8.454897 −0.14453 −0.22004 8.454897 0.496097 −0.51032 8.454897 −0.07751 −0.29149 8.454897 0.423269 −0.44945 8.454897 −0.00832 −0.36111 8.454897 0.351222 −0.38772 8.454897 0.062944 −0.42882 8.454897 0.279868 −0.32513 8.454897 0.136379 −0.49462 8.454897 0.209554 −0.26149 8.454897 0.211982 −0.55843 8.454897 0.140281 −0.19664 8.454897 0.289491 −0.6193 8.454897 0.072048 −0.13057 8.454897 0.368648 −0.67721 8.454897 0.005029 −0.06338 8.454897 0.449279 −0.73244 8.454897 −0.06069 0.005029 8.454897 0.531384 −0.78507 8.454897 −0.12502 0.074562 8.454897 0.614876 −0.83509 8.454897 −0.18597 0.142968 8.454897 0.696808 −0.88122 8.454897 −0.24406 0.209641 8.454897 0.777092 −0.9237 8.454897 −0.29938 0.274579 8.454897 0.855556 −0.9628 8.454897 −0.352 0.337523 8.454897 0.932112 −0.99852 8.454897 −0.40211 0.39856 8.454897 1.00676 −1.03112 8.454897 −0.4498 0.457516 8.454897 1.079155 −1.06103 8.454897 −0.49497 0.514391 8.454897 1.149295 −1.08835 8.454897 −0.53607 0.566498 8.454897 1.217008 −1.11331 8.454897 −0.57352 0.613489 8.454897 1.279085 −1.1349 8.454897 −0.60716 0.655365 8.454897 1.335353 −1.15337 8.454897 −0.63681 0.6923 8.454897 1.385639 −1.16915 8.454897 −0.66265 0.724292 8.454897 1.432891 −1.18328 8.454897 −0.68458 0.751256 8.454897 1.474073 −1.19499 8.454897 −0.70374 0.773971 8.454897 1.505806 −1.20374 8.454897 −0.72065 0.792351 8.454897 1.531209 −1.21059 8.454897 −0.73522 0.80683 8.454897 1.550283 −1.21562 8.454897 −0.74761 0.817581 8.454897 1.564762 −1.21692 8.454897 −0.75784 0.824951 8.454897 1.571958 −1.21328 8.454897 −0.76608 0.829632 8.454897 1.575512 −1.20938 8.454897 −0.77345 0.832407 8.454897 1.576813 −1.20712 8.454897 −0.77978 0.832927 8.454897 1.577333 −1.20591 8.454897 1.527481 −1.38876 9.023823 −0.77536 0.912518 9.023823 1.527654 −1.38815 9.023823 −0.77926 0.90905 9.023823 1.528001 −1.38685 9.023823 −0.78203 0.902634 9.023823 1.528434 −1.38425 9.023823 −0.78333 0.893964 9.023823 1.528174 −1.37896 9.023823 −0.78342 0.88356 9.023823 1.524793 −1.37142 9.023823 −0.78203 0.869688 9.023823 1.512568 −1.36318 9.023823 −0.77891 0.852001 9.023823 1.494535 −1.35477 9.023823 −0.77371 0.830153 9.023823 1.470692 −1.34342 9.023823 −0.76599 0.803969 9.023823 1.440867 −1.32894 9.023823 −0.75568 0.773191 9.023823 1.402373 −1.30978 9.023823 −0.74285 0.737297 9.023823 1.358156 −1.28706 9.023823 −0.72707 0.695247 9.023823 1.311424 −1.26235 9.023823 −0.70825 0.646955 9.023823 1.259318 −1.23365 9.023823 −0.68632 0.592421 9.023823 1.202009 −1.20071 9.023823 −0.66057 0.532078 9.023823 1.139758 −1.16308 9.023823 −0.6304 0.466186 9.023823 1.0756 −1.12216 9.023823 −0.59589 0.394572 9.023823 1.009795 −1.07768 9.023823 −0.55861 0.320443 9.023823 0.942516 −1.02965 9.023823 −0.51821 0.244147 9.023823 0.873676 −0.97815 9.023823 −0.4746 0.166031 9.023823 0.803362 −0.92301 9.023823 −0.42786 0.08592 9.023823 0.731748 −0.86423 9.023823 −0.37749 0.004248 9.023823 0.658833 −0.80189 9.023823 −0.32322 −0.07881 9.023823 0.584705 −0.73582 9.023823 −0.26478 −0.16291 9.023823 0.511703 −0.66854 9.023823 −0.20392 −0.24527 9.023823 0.439742 −0.60022 9.023823 −0.14054 −0.32573 9.023823 0.368562 −0.53104 9.023823 −0.07456 −0.40428 9.023823 0.298075 −0.46107 9.023823 −0.00607 −0.48092 9.023823 0.228628 −0.39015 9.023823 0.064852 −0.55583 9.023823 0.160482 −0.31793 9.023823 0.1382 −0.62892 9.023823 0.093636 −0.24449 9.023823 0.214149 −0.69976 9.023823 0.028091 −0.16993 9.023823 0.292179 −0.76756 9.023823 −0.03615 −0.09416 9.023823 0.37203 −0.83241 9.023823 −0.09884 −0.01725 9.023823 0.453701 −0.8944 9.023823 −0.15987 0.060863 9.023823 0.536933 −0.95379 9.023823 −0.21753 0.13742 9.023823 0.619038 −1.00875 9.023823 −0.27206 0.212068 9.023823 0.699669 −1.05947 9.023823 −0.32365 0.28481 9.023823 0.778913 −1.10612 9.023823 −0.37238 0.355557 9.023823 0.856596 −1.14878 9.023823 −0.41859 0.423963 9.023823 0.932632 −1.1877 9.023823 −0.46263 0.489942 9.023823 1.006847 −1.22299 9.023823 −0.50433 0.55358 9.023823 1.079068 −1.25516 9.023823 −0.54231 0.611669 9.023823 1.149209 −1.28429 9.023823 −0.57716 0.663949 9.023823 1.213887 −1.30926 9.023823 −0.60846 0.710593 9.023823 1.272669 −1.33041 9.023823 −0.63594 0.751862 9.023823 1.325296 −1.3481 9.023823 −0.65987 0.787583 9.023823 1.374889 −1.36379 9.023823 −0.68025 0.817754 9.023823 1.418239 −1.37654 9.023823 −0.69811 0.843158 9.023823 1.451618 −1.38599 9.023823 −0.7138 0.864052 9.023823 1.478408 −1.39336 9.023823 −0.72741 0.880612 9.023823 1.498523 −1.39873 9.023823 −0.73912 0.893183 9.023823 1.513782 −1.40064 9.023823 −0.74891 0.902114 9.023823 1.521498 −1.39708 9.023823 −0.7568 0.908096 9.023823 1.525226 −1.3931 9.023823 −0.76409 0.911997 9.023823 1.526614 −1.39067 9.023823 −0.7705 0.913471 9.023823 1.527221 −1.38945 9.023823 1.466444 −1.60256 9.689679 −0.7679 1.016558 9.689679 1.466704 −1.60187 9.689679 −0.77232 1.013263 9.689679 1.467051 −1.60057 9.689679 −0.7757 1.006674 9.689679 1.467484 −1.59779 9.689679 −0.77761 0.99757 9.689679 1.467137 −1.59216 9.689679 −0.77839 0.986559 9.689679 1.463669 −1.5841 9.689679 −0.77805 0.97182 9.689679 1.451011 −1.57499 9.689679 −0.77614 0.952833 9.689679 1.432111 −1.5658 9.689679 −0.77241 0.929337 9.689679 1.406881 −1.5534 9.689679 −0.7666 0.900986 9.689679 1.375496 −1.53754 9.689679 −0.75854 0.867434 9.689679 1.335093 −1.51638 9.689679 −0.74831 0.828419 9.689679 1.288882 −1.49107 9.689679 −0.73574 0.782381 9.689679 1.240157 −1.46332 9.689679 −0.72082 0.729494 9.689679 1.185969 −1.43098 9.689679 −0.70314 0.669671 9.689679 1.126753 −1.39362 9.689679 −0.68198 0.603345 9.689679 1.062769 −1.35079 9.689679 −0.65667 0.530517 9.689679 0.997223 −1.30397 9.689679 −0.62753 0.45136 9.689679 0.930204 −1.2529 9.689679 −0.59598 0.369255 9.689679 0.862058 −1.19759 9.689679 −0.56138 0.28481 9.689679 0.792958 −1.1382 9.689679 −0.52358 0.198023 9.689679 0.722905 −1.07447 9.689679 −0.48257 0.108982 9.689679 0.651984 −1.00659 9.689679 −0.43775 0.01786 9.689679 0.580196 −0.93445 9.689679 −0.38876 −0.075 9.689679 0.507715 −0.85798 9.689679 −0.33536 −0.16959 9.689679 0.436795 −0.78021 9.689679 −0.27926 −0.26253 9.689679 0.367261 −0.70123 9.689679 −0.22022 −0.35382 9.689679 0.298508 −0.62138 9.689679 −0.15814 −0.4433 9.689679 0.230709 −0.54083 9.689679 −0.09312 −0.53112 9.689679 0.164123 −0.45925 9.689679 −0.02523 −0.61739 9.689679 0.099185 −0.37654 9.689679 0.045257 −0.7021 9.689679 0.03572 −0.29253 9.689679 0.118432 −0.78455 9.689679 −0.02627 −0.20739 9.689679 0.194121 −0.86414 9.689679 −0.08679 −0.12121 9.689679 0.272411 −0.94061 9.689679 −0.14566 −0.0339 9.689679 0.353129 −1.01422 9.689679 −0.20279 0.054534 9.689679 0.436101 −1.08514 9.689679 −0.25655 0.140888 9.689679 0.518639 −1.15112 9.689679 −0.307 0.225073 9.689679 0.600484 −1.21215 9.689679 −0.35426 0.307005 9.689679 0.681722 −1.26842 9.689679 −0.39856 0.386595 9.689679 0.762093 −1.32009 9.689679 −0.44061 0.463498 9.689679 0.841337 −1.36709 9.689679 −0.48066 0.537453 9.689679 0.918847 −1.40948 9.689679 −0.51855 0.608634 9.689679 0.994362 −1.4478 9.689679 −0.55323 0.673572 9.689679 1.067711 −1.48231 9.689679 −0.58505 0.732095 9.689679 1.135423 −1.51153 9.689679 −0.61375 0.784288 9.689679 1.197154 −1.53606 9.689679 −0.63872 0.830499 9.689679 1.252555 −1.55644 9.689679 −0.66048 0.870641 9.689679 1.304922 −1.57439 9.689679 −0.67895 0.904454 9.689679 1.350613 −1.58886 9.689679 −0.69525 0.933065 9.689679 1.385986 −1.59944 9.689679 −0.70955 0.956821 9.689679 1.414337 −1.60759 9.689679 −0.72204 0.975809 9.689679 1.435665 −1.61357 9.689679 −0.73279 0.990548 9.689679 1.451965 −1.61548 9.689679 −0.74189 1.001212 9.689679 1.460201 −1.61158 9.689679 −0.74935 1.008668 9.689679 1.46419 −1.60724 9.689679 −0.75628 1.013957 9.689679 1.465664 −1.60464 9.689679 −0.7627 1.016731 9.689679 1.46627 −1.60326 9.689679

it will also be appreciated that the airfoil 200 disclosed in the above scalable Tables 1-2 may be non-scaled, scaled up or scaled down geometrically for use in other similar turbine/compressor designs. Consequently, the coordinate values set forth in Tables 1-2 may be non-scaled, scaled upwardly or scaled downwardly such that the general airfoil profile shape remains unchanged. A scaled version of the coordinates in Tables 1-2 would be represented by X, Y and Z coordinate values of Tables 1-2, with the X, Y and Z non-dimensional coordinate values converted to inches or mm (or any suitable dimensional system), multiplied or divided by a constant number. The constant number may be a fraction, decimal fraction, integer or mixed number.

The article of manufacture may also have a suction-side nominal airfoil profile substantially in accordance with suction-side Cartesian coordinate values of X, Y and Z set forth in a scalable table, the scalable table selected from the group of tables consisting of TABLES 1-2. The Cartesian coordinate values of X, Y and Z are non-dimensional values convertible to dimensional distances by multiplying the Cartesian coordinate values of X, Y and Z by a number. The X and Y coordinates, when connected by smooth continuing arcs, define airfoil profile sections at each Z height. The airfoil profile sections at each Z height are joined smoothly with one another to form a complete suction-side airfoil shape. The X, Y and Z coordinate values being scalable as a function of a number to provide a non-scaled, scaled-up or scaled-down airfoil profile.

The article of manufacture may also have a pressure-side nominal airfoil profile substantially in accordance with pressure-side Cartesian coordinate values of X, Y and Z set forth in a scalable table, the scalable table selected from the group of tables consisting of TABLES 1-2. The Cartesian coordinate values of X, Y and Z are non-dimensional values convertible to dimensional distances by multiplying the Cartesian coordinate values of X, V and Z by a number. X and V are coordinates which, when connected by smooth continuing arcs, define airfoil profile sections at each Z height. The airfoil profile sections at each Z height are joined smoothly with one another to form a complete pressure-side airfoil shape. The X, Y and Z values being scalable as a function of the number to provide at least one of a non-scaled, scaled-up and scaled-down airfoil.

The article of manufacture may be an airfoil or a variable stator vane configured for use with a compressor. The suction-side airfoil shape may lie in an envelope within +/−5% of a chord length in a direction normal to a suction-side airfoil surface location, or +/−0.25 inches in a direction normal to a suction-side airfoil surface location.

The number, used to convert the non-dimensional values to dimensional distances, may be a fraction, decimal fraction, integer or mixed number. The height of the article of manufacture may be about 1 inch to about 30 inches, or any suitable height as desired in the specific application.

A compressor 2, according to an aspect of the present invention, may include a plurality of variable stator vanes 25. Each of the variable stator vanes 25 include an airfoil 200 having a suction-side 310 airfoil shape, the airfoil 200 having a nominal profile substantially in accordance with suction-side 310 Cartesian coordinate values of X, Y and Z set forth in a scalable table, the scalable table selected from the group of tables consisting of TABLES 1-2. The Cartesian coordinate values of X, Y and Z are non-dimensional values convertible to dimensional distances by multiplying the Cartesian coordinate values of X, Y and Z by a number. The number, used to convert the non-dimensional values to dimensional distances, may be a fraction, decimal fraction, integer or mixed number. X and Y are coordinates which, when connected by smooth continuing arcs, define airfoil profile sections at each Z height. The airfoil profile sections at each Z height being joined smoothly with one another to form a complete suction-side 310 airfoil shape.

The compressor 2, according to an aspect of the present invention, may also have a plurality of variable stator vanes 25 having a pressure-side 320 nominal profile substantially in accordance with pressure-side Cartesian coordinate values of X, Y and Z set forth in scalable Tables 1-2. The Cartesian coordinate values of X, Y and Z are non-dimensional values convertible to dimensional distances by multiplying the Cartesian coordinate values of X, Y and Z by a number. The number (which would be the same number used for the suction side) may be a fraction, decimal fraction, integer or mixed number. X and Y are coordinates which, when connected by smooth continuing arcs, define airfoil profile sections at each Z height, the airfoil profile sections at each Z height being joined smoothly with one another to form a complete pressure-side airfoil shape.

An important term in this disclosure is profile. The profile is the range of the variation between measured points on an airfoil surface and the ideal position listed in scalable Tables 1-2. The actual profile on a manufactured blade or vane may be different than those in scalable Tables 1-2 and the design is robust to this variation meaning that mechanical and aerodynamic function are not impaired. As noted above, an approximately + or −5% chord and/or 0.25 inch profile tolerance is used herein. The X, Y and Z values are all non-dimensionalized.

The following are non-limiting examples of the airfoil profiles embodied by the present invention. On some compressors, each airfoil profile section (e.g., at each Z height) may be connected by substantially smooth continuing arcs. On other compressors, some of the airfoil profile sections may be connected by substantially smooth continuing arcs. Embodiments of the present invention may also be employed by a compressor having stage(s) with no airfoil profile sections connected by substantially smooth continuing arcs.

The disclosed airfoil shape increases reliability and is specific to the machine conditions and specifications. The airfoil shape provides a unique profile to achieve (1) interaction between other stages in the compressor; (2) aerodynamic efficiency; and (3) normalized aerodynamic and mechanical blade or vane loadings. The disclosed loci of points allow the gas turbine and compressor or any other suitable turbine/compressor to run in an efficient, safe and smooth manner. As also noted, any scale of the disclosed airfoil may be adopted as long as (1) interaction between other stages in the compressor; (2) aerodynamic efficiency; and (3) normalized aerodynamic and mechanical blade loadings are maintained in the scaled compressor.

The airfoil 200 described herein thus improves overall compressor 2 efficiency. Specifically, the airfoil 200 provides the desired turbine/compressor efficiency lapse rate (ISO, hot, cold, part load, etc.). The airfoil 200 also meets all aeromechanics, loading and stress requirements.

It should be understood that the finished article of manufacture, blade or vane does not necessarily include all the sections defined in the one or more tables listed above. The portion of the airfoil proximal to a platform (or dovetail) and/or tip may not be defined by an airfoil profile section. It should be considered that the airfoil proximal to the platform or tip may vary due to several imposed constraints. The airfoil contains a main profile section that is substantially defined between the inner and outer flowpath walls. The remaining sections of the airfoil may be partly, at least partly or completely located outside of the flowpath. At least some of these remaining sections may be employed to improve the curve fitting of the airfoil at its radially inner or outer portions. The skilled reader will appreciate that a suitable fillet radius may be applied between the platform and the airfoil portion of the article of manufacture, blade or vane.

This written description uses examples to disclose the invention, including the best mode, and also to enable any person skilled in the art to practice the invention, including making and using any devices or systems and performing any incorporated methods. The patentable scope of the invention is defined by the claims, and may include other examples that occur to those skilled in the art. Such other examples are intended to be within the scope of the claims if they have structural elements that do not differ from the literal language of the claims, or if they include equivalent structural elements with insubstantial differences from the literal languages of the claims. 

The invention claimed is:
 1. An article of manufacture having a nominal airfoil profile substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in a scalable table, the scalable table selected from the group of tables consisting of TABLES 1-2, wherein the Cartesian coordinate values of X, Y and Z are non-dimensional values convertible to dimensional distances by multiplying the Cartesian coordinate values of X, Y and Z by a number, and wherein X and Y are coordinates which, when connected by continuing arcs, define airfoil profile sections at each Z height, the airfoil profile sections at each Z height being joined smoothly with one another to form a complete airfoil shape.
 2. The article of manufacture according to claim 1, wherein the article of manufacture comprises an airfoil.
 3. The article of manufacture according to claim 1, wherein the article of manufacture comprises a variable stator vane configured for use with a compressor.
 4. The article of manufacture according to claim 1, wherein the airfoil shape lies in an envelope within at least one of: +/−5% of a chord length in a direction normal to an airfoil surface location; and +/−0.25 inches in a direction normal to an airfoil surface location.
 5. The article of manufacture according to claim 1, wherein the number, used to convert the non-dimensional values to dimensional distances, is at least one of a fraction, decimal fraction, integer and mixed number.
 6. The article of manufacture according to claim 1, wherein a height of the article of manufacture is about 1 inch to about 30 inches.
 7. An article of manufacture having a suction-side nominal airfoil profile substantially in accordance with suction-side Cartesian coordinate values of X, Y and Z set forth in a scalable table, the scalable table selected from the group of tables consisting of TABLES 1-2, wherein the Cartesian coordinate values of X, Y and Z are non-dimensional values convertible to dimensional distances by multiplying the Cartesian coordinate values of X, Y and Z by a number, and wherein X and Y are coordinates which, when connected by continuing arcs, define airfoil profile sections at each Z height, the airfoil profile sections at each Z height being joined smoothly with one another to form a complete suction-side airfoil shape, the X, Y and Z coordinate values being scalable as a function of the number to provide at least one of a non-scaled, scaled-up and scaled-down airfoil profile.
 8. The article of manufacture according to claim 7, wherein the article of manufacture comprises an airfoil.
 9. The article of manufacture according to claim 7, wherein the article of manufacture comprises a variable stator vane configured for use with a compressor.
 10. The article of manufacture according to claim 7, wherein the suction-side airfoil shape lies in an envelope within at least one of: +/−5% of a chord length in a direction normal to a suction-side airfoil surface location; and +/−0.25 inches in a direction normal to a suction-side airfoil surface location.
 11. The article of manufacture according to claim 7, wherein the number, used to convert the non-dimensional values to dimensional distances, is at least one of a fraction, decimal fraction, integer and mixed number.
 12. The article of manufacture according to claim 7, wherein a height of the article of manufacture is about 1 inch to about 30 inches.
 13. The article of manufacture according to claim 7, further comprising the article of manufacture having a pressure-side nominal airfoil profile substantially in accordance with pressure-side Cartesian coordinate values of X, Y and Z set forth in the scalable table, wherein the Cartesian coordinate values of X, Y and Z are non-dimensional values convertible to dimensional distances by multiplying the Cartesian coordinate values of X, Y and Z by a number, and wherein X and Y are coordinates which, when connected by continuing arcs, define airfoil profile sections at each Z height, the airfoil profile sections at each Z height being joined smoothly with one another to form a complete pressure-side airfoil shape, the X, Y and Z values being scalable as a function of the number to provide at least one of a non-scaled, scaled-up and scaled-down airfoil.
 14. A compressor comprising a plurality of variable stator vanes, each of the variable stator vanes including an airfoil having a suction-side airfoil shape, the airfoil having a nominal profile substantially in accordance with suction-side Cartesian coordinate values of X, Y and Z set forth in a scalable table, the scalable table selected from the group of tables consisting of TABLES 1-2, wherein the Cartesian coordinate values of X, Y and Z are non-dimensional values convertible to dimensional distances by multiplying the Cartesian coordinate values of X, Y and Z by a number, and wherein X and Y are coordinates which, when connected by continuing arcs, define airfoil profile sections at each Z height, the airfoil profile sections at each Z height being joined smoothly with one another to form a complete suction-side airfoil shape.
 15. The compressor according to claim 14, wherein the suction-side airfoil shape lies in an envelope within at least one of: +/−5% of a chord length in a direction normal to a suction-side airfoil surface location; and +/−0.25 inches in a direction normal to a suction-side airfoil surface location.
 16. The compressor according to claim 14, wherein the number, used to convert the non-dimensional values to dimensional distances, is at least one of a fraction, decimal fraction, integer and mixed number.
 17. The compressor according to claim 14, wherein a height of each variable stator vane is about 1 inch to about 30 inches.
 18. The compressor according to claim 14, further comprising each of the plurality of variable stator vanes having a pressure-side nominal airfoil profile substantially in accordance with pressure-side Cartesian coordinate values of X, Y and Z set forth in the scalable table, wherein the Cartesian coordinate values of X, Y and Z are non-dimensional values convertible to dimensional distances by multiplying the Cartesian coordinate values of X, Y and Z by the number, and wherein X and Y are coordinates which, when connected by continuing arcs, define airfoil profile sections at each Z height, the airfoil profile sections at each Z height being joined smoothly with one another to form a complete pressure-side airfoil shape.
 19. The compressor according to claim 18, wherein the pressure-side airfoil shape lies in an envelope within at least one of: +/−5% of a chord length in a direction normal to a pressure-side airfoil surface location; and +/−0.25 inches in a direction normal to a pressure-side airfoil surface location.
 20. The compressor according to claim 18, wherein the number, used to convert the non-dimensional values to dimensional distances, is at least one of a fraction, decimal fraction, integer and mixed number. 